// Copyright 2019 The TCMalloc Authors
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include "tcmalloc/testing/empirical_distributions.h"

namespace tcmalloc {
namespace empirical_distributions {

EmpiricalProfile Beta() {
  static constexpr EmpiricalData::Entry e[] = {
      {1, 1105.1490179533014, 1476.0622627267278},
      {2, 157.89933938068327, 291.72053371223052},
      {3, 6.2577658853964273, 525.96993983526852},
      {4, 593.75976883875342, 939.90755500299713},
      {5, 5.6756481286153644, 235.70437137846059},
      {6, 24.01235413636515, 108.39491152898341},
      {7, 7.34923667936092, 363.01384232844168},
      {8, 5300.9797783872009, 16951.802688542059},
      {9, 6.912750507955189, 49.832559998223921},
      {10, 5.7121154251834749, 145.13278422840398},
      {11, 14.735079440860693, 60.381058100037741},
      {12, 95.577868697747235, 194.60160291277225},
      {13, 32.053343621970313, 30.554270363874519},
      {14, 24.340168985310935, 49.468818684368273},
      {15, 11.642532781151809, 48.741336056656969},
      {16, 10641.957765885396, 18969.844126723354},
      {17, 1811.3512973675154, 2345.7680549696956},
      {18, 323.54434032442515, 2545.2804986346382},
      {19, 980.56477955299943, 1744.6853562151721},
      {20, 768.68323581333891, 2027.8580800568345},
      {21, 963.80493965603387, 1923.1013809026929},
      {22, 928.7464487548159, 2198.2742712519148},
      {23, 306.27905781251735, 1982.7580090136091},
      {24, 4538.3611355990543, 24254.828808027883},
      {25, 1475.1528806333063, 3337.5098017449991},
      {26, 258.90854475001942, 2600.2061474590946},
      {27, 148.75598276838355, 1104.682425682126},
      {28, 625.00204292360127, 1246.541549186333},
      {29, 389.98183130336304, 2249.7407477299471},
      {30, 142.98885385324257, 1726.8623093488445},
      {31, 3514.5618805999979, 6521.3366782851945},
      {32, 39367.795975218447, 125641.79141043003},
      {33, 912.32600175424966, 2367.9069666762871},
      {34, 164.10175424961417, 1684.1736784850032},
      {35, 557.96591426382577, 1950.9254490153853},
      {36, 201.8820578014145, 1016.5667473303288},
      {37, 166.2485982657355, 1321.7550229780431},
      {38, 149.49885085547425, 1192.0166618564483},
      {39, 164.82936258563069, 1330.4850809226739},
      {40, 15252.584708050674, 46808.024443309725},
      {41, 134.47133467307671, 1267.6771640432476},
      {42, 113.01536633839252, 868.64076549075332},
      {43, 102.28169140750775, 899.07471749217416},
      {44, 130.9903949282201, 1114.9011500122106},
      {45, 260.77869474946431, 787.64522789334637},
      {46, 106.30844926554676, 643.59927180694},
      {47, 119.72255321038783, 866.2157493950225},
      {48, 12180.187452674121, 56104.690295939436},
      {49, 435.77676396460413, 625.81707479519571},
      {50, 138.91348884719153, 365.46915169948716},
      {51, 149.22899952257762, 746.94291010811889},
      {52, 715.47611333784846, 352.10164731478807},
      {53, 121.58456038282611, 929.90500188708563},
      {54, 120.26555564191102, 442.67336767089228},
      {55, 137.58520545815892, 605.44809404346961},
      {56, 7487.5934859604513, 29558.180050174276},
      {57, 158.21633228596488, 946.18353573252227},
      {58, 213.13206612854876, 720.66319960926228},
      {59, 154.30481197330877, 679.01445285615966},
      {60, 155.68755482030045, 333.18719889883},
      {61, 679.007747565701, 567.4366161223719},
      {62, 192.42843327744902, 385.020635836867},
      {63, 167.93117679061143, 614.26867659791753},
      {64, 7468.7024959197042, 18537.277457096552},
      {65, 162.52274084847946, 623.05414825833088},
      {66, 131.35891836077587, 177.66210065936994},
      {67, 149.53173859460179, 577.00168727660241},
      {68, 176.87499084015232, 251.43334147370291},
      {69, 169.88786125884064, 388.42668117132519},
      {70, 147.19567988275395, 204.6533534622472},
      {71, 184.31262837665292, 790.89463401638432},
      {72, 2069.818872617052, 27739.735030970405},
      {73, 181.52539220802291, 502.50291943254223},
      {74, 180.21503325302274, 182.53653175854183},
      {75, 177.94164566378362, 409.67049264036586},
      {76, 166.60503736107563, 203.7803210265746},
      {77, 178.65802902283855, 437.53475567790775},
      {78, 160.51424939211921, 188.06573718446816},
      {79, 174.13827706041059, 350.59528672601738},
      {80, 1520.087034096839, 16502.423018005018},
      {81, 172.12504135810008, 359.23728437271052},
      {82, 150.63299099559217, 199.07586084408231},
      {83, 166.52165276960486, 303.03867415580669},
      {84, 217.89903183185851, 205.92584863352795},
      {85, 172.28280502292736, 420.70207357414029},
      {86, 149.7839808142827, 195.55969851031236},
      {87, 165.86063597099937, 334.07606065315366},
      {88, 1119.4833701577713, 4292.5027862264951},
      {89, 153.56208489235792, 383.84568079390806},
      {90, 143.15561637447678, 225.93046644317653},
      {91, 164.71446922846326, 329.1053770841196},
      {92, 209.60901440039083, 229.264658215483},
      {93, 144.11985521889261, 348.92810203583241},
      {94, 152.38559738861071, 219.08026774415558},
      {95, 523.585947128249, 359.35455009657437},
      {96, 2301.4902605837874, 7016.515240991941},
      {97, 523.30760655956124, 461.15823768399088},
      {98, 139.66411671311357, 265.679128832449},
      {99, 150.74179888305372, 290.93228692582642},
      {100, 157.51004141361432, 211.69103967320117},
      {101, 147.49803035518002, 333.85246320182938},
      {102, 144.82088112183152, 210.08024554314767},
      {103, 156.12208911143927, 299.86968008347577},
      {104, 681.22787813516607, 5039.9097973047974},
      {105, 152.77955855085659, 324.13568145993827},
      {106, 130.68137275583732, 240.4258042315121},
      {107, 134.49176612965903, 289.47788779610596},
      {108, 136.05646241131603, 225.87958173301067},
      {109, 132.71392629931051, 246.35236329729369},
      {110, 132.39681903471859, 216.31655307150945},
      {111, 131.19600852698548, 225.6166884976578},
      {112, 984.79636714890023, 6497.7286148791154},
      {113, 140.59958808442605, 256.25587771684832},
      {114, 121.46731988408629, 191.82825300268632},
      {115, 124.76975806899308, 211.74299003174744},
      {116, 210.41236968034909, 200.73978198610217},
      {117, 139.78981424939212, 231.20325022756032},
      {118, 131.42916828583165, 204.15005661257021},
      {119, 132.87568032686778, 225.97454654441313},
      {120, 1009.1300987042979, 10500.910796350154},
      {121, 586.10452440960614, 213.10704215971404},
      {122, 123.83707129137198, 174.09574184667983},
      {123, 131.90677717699046, 191.9645005883267},
      {124, 125.02443625301164, 180.96131474368937},
      {125, 166.93204725371112, 199.37579646115933},
      {126, 117.96005973330965, 155.13573696245808},
      {127, 144.72053582333152, 180.14297449104188},
      {128, 2498.9147734464345, 7599.8978753635411},
      {129, 149.45667336538355, 191.09126834358281},
      {130, 100.14078741381417, 135.88179073329928},
      {131, 123.36336171960873, 139.9638456585929},
      {132, 99.340168985310939, 153.09934951046779},
      {133, 132.04886584431588, 152.250593876962},
      {134, 96.246770737339986, 123.7970716870546},
      {135, 122.45355013489957, 159.52564216415425},
      {136, 611.35250313655388, 1408.5711320293942},
      {137, 131.915188692862, 152.45267855160625},
      {138, 95.482501915240874, 117.45161290322581},
      {139, 115.9716055825108, 133.61838687476413},
      {140, 86.926176068926466, 130.02127966609683},
      {141, 131.47842939145303, 124.96916279999112},
      {142, 89.053121565057126, 111.75282507825855},
      {143, 116.66303418566179, 120.56371689274692},
      {144, 405.4479431978416, 3802.4055125102682},
      {145, 125.32929485827218, 120.22384166241147},
      {146, 80.807690941188227, 101.23538618653286},
      {147, 104.79925166820256, 107.92863486002264},
      {148, 76.138268178134055, 105.78244122283152},
      {149, 102.84486437874027, 114.0398619097307},
      {150, 79.315592836443983, 105.92793552827298},
      {151, 93.909894856051608, 99.707579424105859},
      {152, 129.20103478521546, 608.28538285638172},
      {153, 99.69301519979571, 99.598450369646784},
      {154, 72.345921369647044, 87.630630730635175},
      {155, 93.342123086146984, 96.288202384388256},
      {156, 72.982842772602623, 92.286803720888926},
      {157, 95.83516604305683, 88.794673978198617},
      {158, 77.219126872217345, 91.886663854539},
      {159, 96.311944441360325, 93.669105077370517},
      {160, 626.70819945151948, 2883.2987811646649},
      {161, 92.598518880389037, 83.530781697489061},
      {162, 67.30418688309814, 79.727915547365853},
      {163, 88.25441726714557, 83.563850098794489},
      {164, 69.487797972620385, 77.5784694625136},
      {165, 96.009669468284727, 87.465921452833953},
      {166, 71.171984189547786, 79.893257553892951},
      {167, 89.108045121964764, 80.918377994360938},
      {168, 355.29312400768316, 1098.929123282197},
      {169, 92.022825230106477, 82.9024820726861},
      {170, 66.5365883175858, 80.918377994360938},
      {171, 85.058212219791926, 75.660502186799278},
      {172, 64.1444102723528, 80.455420376085073},
      {173, 89.67360187416034, 78.405179495149085},
      {174, 55.948984644764451, 73.24650889150368},
      {175, 73.86849456515705, 63.822014519459181},
      {176, 1861.8626833357389, 1875.3427502608617},
      {177, 79.056212597288692, 71.756732455653491},
      {178, 55.612138741159356, 65.8452145727416},
      {179, 76.690263914641321, 71.241369358168868},
      {180, 51.944954311790113, 64.117232422351975},
      {181, 66.980854252945036, 62.3286193193171},
      {182, 47.391983745433954, 53.840285948982086},
      {183, 69.953479076687358, 64.026285993384093},
      {184, 485.17640312212018, 1897.1122149945606},
      {185, 72.307304562159288, 60.964422884798971},
      {186, 54.319844116046944, 57.023410962857717},
      {187, 64.984995614375961, 54.264702617498834},
      {188, 41.006970366504937, 46.807095442133075},
      {189, 61.627100935969892, 44.26059543103257},
      {190, 37.655136731544296, 38.015607308571809},
      {191, 58.366276216594315, 37.985291832249182},
      {192, 493.07094385290952, 1475.0904469062896},
      {193, 55.687331653102689, 41.116288879515132},
      {194, 28.930808176135542, 30.228037652909443},
      {195, 51.464423151653769, 36.380791687942633},
      {196, 29.362651137486537, 32.586794840485759},
      {197, 49.951501659875426, 34.26390338121351},
      {198, 25.033225265635583, 27.605421486135469},
      {199, 46.36400013323415, 33.704204870901137},
      {200, 39.645868075987877, 830.02111315853745},
      {201, 43.199431534302242, 29.988166862775572},
      {202, 21.252032375897944, 23.209744022378615},
      {203, 40.921271941998732, 27.557445108007904},
      {204, 18.490564801758691, 23.519581288990519},
      {205, 41.510649849556444, 31.833192726949804},
      {206, 18.192327933649395, 19.727582532246963},
      {207, 36.188195454494988, 23.907377394933729},
      {208, 44.813453318085422, 720.35680349887889},
      {209, 36.728739715989207, 30.920209577514818},
      {210, 13.175623702354914, 29.19818839775326},
      {211, 32.279706218703851, 25.776657860266855},
      {212, 11.129179388677318, 14.994083431387786},
      {213, 30.758575282844994, 25.284650223120131},
      {214, 10.593349395450053, 16.490897586750439},
      {215, 27.367326545793688, 21.901238816242259},
      {216, 242.39429757846935, 365.58234353839663},
      {217, 29.31477122586519, 23.541837799436095},
      {218, 9.03076820589117, 14.188508758297626},
      {219, 28.451791444147133, 22.166296649867903},
      {220, 8.0393473747321433, 16.293397420242879},
      {221, 30.443981702510353, 33.574273472015626},
      {222, 7.07535723405909, 14.235286281997203},
      {223, 23.534559827683836, 18.08645072486291},
      {224, 191.59234014677961, 1104.35288502098},
      {225, 24.506073256575661, 27.043880292165266},
      {226, 6.6501659875426071, 10.914570521501677},
      {227, 23.401778675874628, 23.623981528761405},
      {228, 6.7375476034507642, 11.011588926137247},
      {229, 24.158957220735676, 25.176276002930532},
      {230, 5.3759734419931826, 15.110616521990098},
      {231, 21.712525120188303, 19.112625713207379},
      {232, 159.01765685545206, 1249.3302510933997},
      {233, 29.376841684523743, 21.368303620984392},
      {234, 5.1332508021805987, 9.3380214461736557},
      {235, 23.93329188270954, 18.967098106254024},
      {236, 7.63313311201661, 9.532058255444797},
      {237, 24.027907002564756, 22.023177852274493},
      {238, 4.361440927309669, 9.1682392380614086},
      {239, 21.372753616751975, 15.765490753280199},
      {240, 59.246393240587565, 374.19404790977512},
      {241, 206.30104366749197, 20.142286259796194},
      {242, 4.3201561060099705, 5.4788646404546766},
      {243, 25.044885474147023, 13.458450813666941},
      {244, 4.0084825740837378, 5.8198721221943472},
      {245, 23.111249403222047, 16.64118730990387},
      {246, 3.4260961284377185, 4.0466332171480586},
      {247, 22.911066206268668, 11.617010412272718},
      {248, 6.7884852387666959, 327.03002686321958},
      {249, 24.960579346486504, 15.390837644029039},
      {250, 3.3510220169429425, 2.2961170437137848},
      {251, 21.011412615053239, 10.343893612770019},
      {252, 2.9165032697880466, 11.298736762649025},
      {253, 24.7194510753106, 13.162899895655263},
      {254, 2.8710026979914951, 2.0233110583220477},
      {255, 17.78104522189037, 7.4794307661567832},
      {256, 1239.1681059655589, 1423.5657482849722},
      {257, 25.383246916184618, 77.41020802344427},
      {258, 2.8163744767783983, 1.4339186999089759},
      {259, 15.480361286597756, 7.8116466487578533},
      {260, 2.6493188404187995, 2.6324179117731945},
      {261, 19.283964160014211, 14.703017116977112},
      {262, 2.2359665582288741, 3.9807295251204406},
      {263, 15.94510197963738, 10.144439757564994},
      {264, 191.65329699001853, 402.97156050884712},
      {265, 22.429919948482794, 10.058832671003264},
      {266, 2.2809253111572496, 0.898874408898164},
      {267, 14.880705474813194, 7.1909952711853116},
      {268, 2.7692551100847149, 1.0914903536620562},
      {269, 15.921538410294559, 10.829296450058832},
      {270, 2.0988963771414615, 0.85607086561729906},
      {271, 14.313135776699568, 7.0411828697022845},
      {272, 157.81203770526386, 350.79643895832874},
      {273, 18.534401056990905, 11.086905845525386},
      {274, 2.0255698535534656, 2.2786559509801747},
      {275, 14.587079618506223, 8.0806118597784344},
      {276, 2.0025636470627424, 0.63189618808693915},
      {277, 15.422546548680426, 11.565615078924584},
      {278, 1.8396904526630176, 0.45956086406322849},
      {279, 14.922437740792965, 6.87426459161246},
      {280, 116.47573473081151, 69.757509490930886},
      {281, 18.591985966003087, 12.580478653730879},
      {282, 1.8588561848401746, 1.6850565015651711},
      {283, 13.061701844182664, 6.0891814488377776},
      {284, 1.8301075865744389, 1.6276113935572676},
      {285, 15.556712225343356, 11.699653664276358},
      {286, 1.7649527573917194, 1.0914570521501676},
      {287, 12.49257774767673, 8.8465466332171481},
      {288, 64.028333351838072, 109.09036920276181},
      {289, 18.222155728513219, 12.293253113691362},
      {290, 1.6691351993515937, 0.97656683613436046},
      {291, 11.881231749697447, 8.02316675177053},
      {292, 1.5867276582988219, 0.76593477343871408},
      {293, 12.827907002564757, 12.771962347090557},
      {294, 1.4660030865910934, 0.5553027107430677},
      {295, 10.942258540864023, 8.38698576915392},
      {296, 185.72583854241842, 1070.2367959505361},
      {297, 13.211068426837798, 12.925149301778301},
      {298, 1.3951003142105323, 0.86167662011855339},
      {299, 10.997846047942087, 8.46357924649779},
      {300, 1.9392319051372866, 9.1146238039206988},
      {301, 12.5826151642666, 15.6059210088138},
      {302, 1.5522399991117724, 0.5553027107430677},
      {303, 10.474691063319529, 16.735674799635902},
      {304, 85.837188981535974, 2353.1594143374109},
      {305, 12.028090199518136, 16.797426903181403},
      {306, 1.4021217538055004, 0.90047288146881865},
      {307, 9.9431056879878312, 11.844792753591014},
      {308, 1.6308969989008182, 0.675354661101614},
      {309, 12.802810130236379, 16.676220500410718},
      {310, 1.3362618939234125, 0.62341540305929888},
      {311, 10.189213585441948, 10.390182714295229},
      {312, 89.581541519091346, 1002.954554536776},
      {313, 11.542807021439595, 14.407699309548654},
      {314, 1.3605260528273397, 1.29875896365695},
      {315, 11.345227441793332, 11.048187287702861},
      {316, 1.4350516837465443, 3.0650711542304019},
      {317, 11.345227441793332, 17.66327731279},
      {318, 1.4107875248426172, 0.883156095286726},
      {319, 10.839146413225709, 8.9875008325377976},
      {320, 31.67339314066195, 512.03997291477037},
      {321, 13.222233448432833, 16.399063117465534},
      {322, 1.9809952590849034, 3.3421508336478478},
      {323, 10.052294403055503, 12.606698044091202},
      {324, 2.2305694649538679, 4.2772572874808512},
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      {3421, 3.4937857372844654, 7.6334502586417434},
      {3528, 1.4973708461478681, 19.420697999689178},
      {3584, 2.9858238866621516, 8.6236818151544057},
      {3696, 1.685035584620338, 12.064649335079809},
      {3848, 1.27709371912021, 8.430244433097263},
      {3968, 0.99644930995814229, 5.901039007170926},
      {4044, 0.69294303129892187, 5.6806829030037953},
      {4096, 174.59395561082297, 15.782041604688853},
      {4097, 947.15749941710055, 0.045589769775547809},
      {4099, 0.23957387278359443, 0.029571742557112094},
      {4112, 0.0793498173581889, 1.3384876673400974},
      {4200, 0.5836088689531127, 4.0500965743844768},
      {4240, 0.23070491967091172, 1.6693714894656222},
      {4248, 0.037868475690319425, 1.1733454698843329},
      {4368, 0.75162823231594234, 4.9006171880203375},
      {4388, 0.17774101502215012, 1.3204049463845657},
      {4536, 1.0739516137986169, 3.6675288058077831},
      {4608, 0.44164455349906179, 1.7113979974690854},
      {4704, 0.58766695904160249, 3.5084474835157509},
      {4800, 0.53120676829471414, 8.5881602024731887},
      {4872, 0.37856484617007335, 1.6838798481451058},
      {5040, 0.80573017864478647, 3.35834646892969},
      {5096, 0.255537544272597, 1.3858091157338546},
      {5120, 0.20377163667047868, 1.55997602291144},
      {5121, 77.971702177268028, 0.0087027951068978527},
      {5128, 0.029706773846136764, 1.061741003041538},
      {5208, 0.39424650537932882, 4.2856492684767895},
      {5336, 0.73975373888327611, 2.3415181049219629},
      {5376, 0.33560793631407726, 1.6884421552738496},
      {5408, 0.13928852965014932, 36.991374908420852},
      {5424, 0.065014933327411831, 15.230879381923939},
      {5440, 0.094511863390587, 17.262848833337035},
      {5456, 0.098909700556252575, 7.3568034988788487},
      {5472, 0.10854030888116623, 2.9801522989143705},
      {5560, 0.53730112027712718, 42.388451035677022},
      {5712, 0.81838076098904167, 3.4195546477810104},
      {5768, 0.31864722928486572, 1.3700241990986388},
      {5880, 0.619099115103201, 4.2148502542015409},
      {6048, 1.1457126361486449, 2.6504784317207983},
      {6144, 0.62064463121898128, 132.92952290033969},
      {6152, 0.057043090144003911, 16.333681149124171},
      {6424, 1.9803068826540238, 3.721854672202118},
      {6841, 6.03571341334784, 6.2108429722709433},
      {6888, 0.5870130014322672, 1.4059565304264812},
      {7160, 3.2733864789545564, 12.048176187198894},
      {7168, 0.85696203937069071, 1.7184912195013653},
      {7763, 5.9047453562348009, 5.3575916346602144},
      {7793, 0.48201672088556297, 0.78762515818218148},
      {7823, 0.29968467918327463, 0.35325133761072752},
      {8000, 1.3182497474102612, 6.9886774859578624},
      {8192, 234.24888471915349, 27.603423395422148},
      {8193, 1.0040780752106766, 0.0028306285105343782},
      {8200, 0.043264458680759878, 2.5900250871389559},
      {8208, 0.060695926365927577, 1.4490264858024555},
      {8248, 0.3169107442237446, 2.2624381146904069},
      {8352, 0.79786159192601069, 1.3421952356636988},
      {8488, 0.90312323048397281, 1.2019514685966743},
      {8648, 1.0807665404643205, 1.8793819239393468},
      {8736, 0.60635859970910544, 1.3599449415003442},
      {8760, 0.14621115391874936, 1.0651044557422902},
      {8904, 0.98021139818135417, 1.4062229425215906},
      {9216, 2.2001265724405177, 2.9266700708212157},
      {9240, 0.16304417822287856, 1.0144972581755214},
      {9576, 2.3896843460979049, 2.15213240681127},
      {9728, 1.077360187416035, 1.4396798614657109},
      {10072, 2.446778509331943, 30.725406833470238},
      {10080, 0.0555775145169707, 1.1096507781453278},
      {10568, 3.5167775100758325, 2.0356992207446218},
      {11136, 4.175773590771314, 6.1297759918300283},
      {11264, 0.89481830193078438, 1.4314876895411048},
      {11880, 4.475929030610545, 2.5030748395977169},
      {12288, 3.0473725115747174, 6.1203516639655415},
      {12296, 0.062897620660175207, 2.7620828985635946},
      {12344, 0.3447444680071502, 4.1934595830650681},
      {13944, 11.529968801003696, 4.1379903647625591},
      {14336, 3.2149288862735514, 1.0719756676953136},
      {14448, 0.73865011602473729, 0.56411651088959425},
      {14784, 2.1829904404498879, 1.0899473836112155},
      {15120, 2.0779131091298706, 1.3336922496281327},
      {16384, 8.157245161935, 2.5589880780587428},
      {16385, 0.80427570586341279, 0.00057722620606975557},
      {16392, 0.034161235524664969, 2.5643274204648887},
      {16640, 1.2131335561304357, 1.341762316009145},
      {16983, 1.6853264791766123, 1.0398730102346641},
      {18440, 6.9303296434876245, 3.8437493062185015},
      {20480, 9.104485549646375, 2.8656395000333013},
      {22536, 6.8929863323969958, 2.8205270519281567},
      {22584, 0.15034474335772258, 1.9180782807539463},
      {24584, 5.9287774656644485, 3.9003174744133382},
      {24632, 0.11775789134755238, 0.96888528739204771},
      {28672, 6.8615452940588693, 1.0200142086450723},
      {28736, 0.067513073600763876, 1.0528828008791598},
      {30000, 3.6150265913153552, 0.33573474235730294},
      {30209, 0.30546037949526467, 0.2634482605510291},
      {30488, 2.4579657366182968, 0.061019470283950904},
      {30523, 0.052331042446178949, 0.9756232932975154},
      {30532, 0.0074977516737539827, 0.13433829895877272},
      {30666, 0.14391508543639733, 0.19031814044357617},
      {32756, 2.4954989063697033, 1.8358235463890065},
      {32768, 1.187823509165399, 16.266412095109121},
      {32769, 0.73978926798938571, 0.0012432564438425505},
      {32784, 0.0029577980836488389, 0.94207757032169259},
      {32816, 24.066424994726148, 0.00901360921785849},
      {34776, 1.1133245250757771, 1.3186066647425791},
      {36287, 0.46238355890614752, 0.23494216637435353},
      {36872, 0.14096616962927597, 2.7100881380014687},
      {45064, 1.0694172116313414, 2.7280709544213293},
      {45552, 0.021138707850822173, 0.45044735030970384},
      {45600, 0.00067727358521989191, 0.53006016473147888},
      {49208, 0.088439717099492568, 1.1727793441822263},
      {50680, 0.04959419099115104, 0.32451213285083125},
      {51708, 0.026331508765696652, 0.24037031281220153},
      {51713, 0.00023649061254399503, 0.10101458606220723},
      {55455, 0.086526696792387892, 1.4610261305863292},
      {57352, 0.013003652836221919, 0.10085917900672692},
      {60417, 0.038082760611544766, 0.35116444286570658},
      {65536, 121.74173670711809, 7.3141664631574352},
      {65537, 0.37111150587895675, 0.98954332526696709},
      {65544, 0.020383714345986875, 0.00062162822192127524},
      {71904, 0.012516237911776787, 1.00081033678929},
      {74256, 0.0055625256753305862, 3.84054126057323},
      {77824, 1.4966169629275983, 0.14864684856692492},
      {81920, 0.02843549801814205, 0.91923273316608578},
      {104864, 0.032481374976406435, 0.10222454099416112},
      {114688, 0.0034851832524676069, 1.0047066136802631},
      {131072, 0.0979315398536644, 0.9405234997668892},
      {135688, 0.0018319695337915096, 0.91081855116222366},
      {262112, 0.020599109551778128, 0.054514574961703297},
      {262144, 0.066030843705241649, 0.73505317141398219},
      {262145, 24.377668846525363, 0.0015096685389516685},
      {524288, 0.38828427726026177, 0.045556468263659167},
      {1048544, 0.0030888116624290807, 0.00014430655151743889},
      {1048576, 0.0511752362130414, 0.0010656483804364718},
      {2097152, 0.0185528550967613, 0.0011100503962879914},
      {3145728, 0.00064840618650560135, 8.8804031703039322e-05},
      {4194304, 0.0044555719630941411, 0.00099904535665919225},
      {8388608, 0.00027090943408795672, 0.00019980907133183848},
  };
  return e;
}

EmpiricalProfile Bravo() {
  static constexpr EmpiricalData::Entry e[] = {
      {1, 811.78292031630951, 457.35138608644246},
      {2, 273.58155161960292, 21181.404631854926},
      {3, 286.0939472903417, 2937.8301481833723},
      {4, 10816.429176072963, 16546.356436916038},
      {5, 7231.1829216063161, 9843.5975272783362},
      {6, 2732.252029824946, 2877.1905178064235},
      {7, 2200.5626310968923, 510.41420658278605},
      {8, 100757.74352739328, 163657.13637239908},
      {9, 1562.071031618055, 365.96527394003266},
      {10, 1482.3892090971246, 387.86470716755133},
      {11, 679.94649311781632, 444.71742343430708},
      {12, 2657.3009971748861, 10531.359341464355},
      {13, 779.92040015996076, 717.19096762585309},
      {14, 676.56516079928792, 351.64687889575754},
      {15, 409.57489389698009, 296.89933041164903},
      {16, 33261.498097240677, 366425.41487488593},
      {17, 17055.050386356892, 32397.320399953733},
      {18, 12886.807994169172, 68902.237684586609},
      {19, 25561.385053986764, 71965.3980259353},
      {20, 23087.824226318709, 69779.875759873539},
      {21, 14349.386867735651, 32663.25098638975},
      {22, 8525.2044698719019, 21030.720752098085},
      {23, 12879.145773294289, 28104.826215476358},
      {24, 44242.930638940132, 972750.54570808},
      {25, 6294.7429443104274, 9903.8355845724782},
      {26, 5825.6107289825723, 37728.555886851136},
      {27, 4912.6335259742773, 11587.35179734992},
      {28, 32818.314720262126, 12201.16527651043},
      {29, 12540.485745430153, 6562.3417599506483},
      {30, 5092.508960383906, 10015.069413563984},
      {31, 100374.07516737832, 273484.02981660218},
      {32, 427330.66193449346, 2149933.3716408126},
      {33, 9520.28678775526, 74017.452942461663},
      {34, 5639.1956165585216, 11648.223650220412},
      {35, 9503.74446522788, 8429.8169491961089},
      {36, 5809.680554444717, 7221.4033980644908},
      {37, 5510.694185941511, 9611.4095284607174},
      {38, 5494.2295708148968, 11294.890770990502},
      {39, 4872.9702601942754, 23739.203819609556},
      {40, 99018.366977128186, 724178.81835006236},
      {41, 6058.0230691830393, 12791.211453687876},
      {42, 3204.9019491995509, 9376.2735030651984},
      {43, 4143.33752241386, 10154.840815329846},
      {44, 4616.260094944465, 10099.379878934313},
      {45, 3447.5912344070484, 12892.572363094243},
      {46, 2266.102447141991, 9036.4089629734353},
      {47, 2316.3839561913856, 7405.4474546646279},
      {48, 171553.40227299114, 1384246.6163811383},
      {49, 3082.592815954798, 634945.20613296668},
      {50, 6378.6578619435231, 11366.450307805009},
      {51, 1680.2321701776339, 8297.2215553470687},
      {52, 9158.2035307473016, 6916.2859566374073},
      {53, 2427.3174744256248, 6092.9389273734405},
      {54, 1841.5216966163134, 4637.5836471359353},
      {55, 23821.993413227723, 4937.8283617576371},
      {56, 53661.749976134881, 866183.41556889308},
      {57, 1745.5032056657078, 6718.4278039815445},
      {58, 1526.3306570002194, 6296.0779472811628},
      {59, 2644.2549374991936, 4749.6022311043707},
      {60, 1454.9410234910151, 5703.390880232364},
      {61, 23239.412078329184, 15753.390430412934},
      {62, 1016.0133464053974, 6390.9438239792316},
      {63, 1016.3454056424877, 5209.7998689097658},
      {64, 217689.27808795264, 1468747.9046125771},
      {65, 2091.3826300648875, 4954.9405724273538},
      {66, 745.34866548846094, 6468.75640350088},
      {67, 1017.4310620622041, 4802.2296520968011},
      {68, 1427.2561707452367, 2607.735981698775},
      {69, 1208.9387621099343, 4629.4682363222764},
      {70, 782.84811852578082, 2434.385495251192},
      {71, 1077.9312362130574, 3856.3885154673626},
      {72, 66236.23898528103, 2030584.0648768137},
      {73, 1654.6904371831422, 3540.9407652071095},
      {74, 1590.0750693378398, 2798.4357079515221},
      {75, 1741.8607838078406, 3176.4689046254289},
      {76, 1259.0317986558134, 3032.9374236913468},
      {77, 1363.3106012719463, 3574.8855659371025},
      {78, 690.40158025774326, 2328.0851315400532},
      {79, 1253.8296043550613, 2233.3242298448768},
      {80, 99898.253726183262, 481580.38352889771},
      {81, 2930.713634076807, 8167.3501137400553},
      {82, 825.02114707362068, 5159.32226349137},
      {83, 1074.6100749493673, 1946.8995231914046},
      {84, 676.69042170306636, 1597.7886748319604},
      {85, 1660.120806511952, 1627.1171586834428},
      {86, 525.14445361782271, 2293.7495148376152},
      {87, 856.83206310710921, 1584.793108766338},
      {88, 98144.624083128, 54408.472040509456},
      {89, 957.861170809737, 1605.4972946574303},
      {90, 460.52545182471397, 1305.5427649757739},
      {91, 1137.5271752731589, 1319.5042604325977},
      {92, 716.835031411654, 1200.6141063373132},
      {93, 814.59890607463979, 1550.4153504093356},
      {94, 442.31241631083992, 1077.4940045496023},
      {95, 773.25362685277162, 1161.1489673431095},
      {96, 58043.396117080971, 297617.03653818968},
      {97, 760.06812781382632, 1519.786605662584},
      {98, 524.66355216140562, 1260.4381241244587},
      {99, 619.62252867039047, 1476.3582361937565},
      {100, 486.87058398586151, 1114.783829634104},
      {101, 685.8118229079322, 1770.7417265354907},
      {102, 402.79399760058823, 2086.9809790641184},
      {103, 666.39418078148583, 1510.5301057718259},
      {104, 34590.795068305837, 115823.68779961187},
      {105, 570.75049858744308, 1720.5653073551903},
      {106, 318.80005289025917, 1280.8291457286432},
      {107, 533.39525535675125, 1563.5292575409014},
      {108, 467.65065596821427, 1331.0673443946073},
      {109, 12221.370166023813, 18520.87979539642},
      {110, 586.04790567473776, 1575.000565487283},
      {111, 854.85732401088762, 11569.458468814662},
      {112, 41953.006195900358, 225068.7049698621},
      {113, 882.62103742308341, 7144.704712822424},
      {114, 481.64667500870752, 1893.2714081918543},
      {115, 1049.0670467885293, 1202.6779935483041},
      {116, 763.11247952114968, 1134.5581488002674},
      {117, 664.3687973271069, 1265.2111966482028},
      {118, 301.98907622647351, 1207.0397897415467},
      {119, 532.30745494652922, 1948.0474752278014},
      {120, 8092.5646357667156, 54718.53064555514},
      {121, 5252.0638901430621, 3497.7701037155084},
      {122, 246.2870509165495, 2209.5322006451697},
      {123, 455.45039538693737, 2237.2652135357093},
      {124, 267.04253021839804, 2075.920369108972},
      {125, 460.93581831550972, 2112.7697567119485},
      {126, 205.48770236974161, 2304.7072061072627},
      {127, 504.12000928804554, 3651.0452903905716},
      {128, 61097.870029283142, 427283.27776992379},
      {129, 815.22268992118063, 2958.3048490534516},
      {130, 247.18471729511475, 2435.5109820200746},
      {131, 456.763019388795, 2179.0283643280341},
      {132, 574.84537984236124, 2257.1776015628011},
      {133, 559.01912047369035, 2289.7479597475872},
      {134, 189.28003328216309, 2161.4825662841058},
      {135, 375.63020936802593, 2102.04719248416},
      {136, 11872.259231930237, 27372.789613026769},
      {137, 467.95210722532539, 2177.7711575781723},
      {138, 174.02397347747004, 2171.8816460820726},
      {139, 396.10076110372938, 2476.42001567942},
      {140, 201.72277893161677, 2671.2320682697373},
      {141, 479.00013158064473, 2244.5401560230821},
      {142, 234.47278602665153, 2259.3738513539565},
      {143, 371.09672725396354, 2470.5093755221119},
      {144, 3275.9860098814484, 23968.336169337737},
      {145, 489.41883667229968, 2196.1860453160944},
      {146, 195.04410531611606, 1926.8107031320285},
      {147, 417.60294379442462, 2116.3338688326544},
      {148, 191.60270901327416, 2143.2482360652366},
      {149, 441.06971839162014, 3392.3127273194618},
      {150, 174.12201266786207, 2139.4982328522406},
      {151, 386.34906281040776, 2221.4999421660732},
      {152, 2338.98079180588, 53378.663033839272},
      {153, 455.42271701131335, 2819.8126951895024},
      {154, 233.93639494833525, 2518.3058001002455},
      {155, 321.17317302854786, 2606.3287794471075},
      {156, 259.08367755002, 2628.9108843449985},
      {157, 401.81465963183217, 2857.5651402794019},
      {158, 153.81246662108646, 2786.7758742561914},
      {159, 326.61665914162978, 2957.3841200889356},
      {160, 24540.653051509951, 124216.99537328587},
      {161, 442.91651208090917, 3452.0285956637408},
      {162, 180.19542821759828, 3608.2171599686412},
      {163, 301.43736761310129, 3847.0898353660887},
      {164, 272.83347695403705, 3650.3134213265816},
      {165, 360.25705826958551, 3873.2734259532958},
      {166, 140.78069892542473, 3786.7667107918105},
      {167, 276.31210928933552, 4157.097006772995},
      {168, 3339.5434951431262, 30622.530015807941},
      {169, 337.42946761439129, 4283.2710740402781},
      {170, 136.20739818625111, 5062.9768921333007},
      {171, 284.68523071763053, 6208.0647997018341},
      {172, 147.62414246829809, 6603.269647470087},
      {173, 284.42178433674326, 6388.2770887686511},
      {174, 130.84134212257641, 5620.7755529565984},
      {175, 272.20450212206038, 5107.9532958912205},
      {176, 2692.9944129826235, 44224.536724543432},
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      {8097, 0.83988570543995666, 128.95882224421339},
      {8098, 0.79954720778131816, 129.83381099872764},
      {8099, 0.78432900321211574, 130.18691925098639},
      {8100, 0.81048517137733977, 131.50294953026},
      {8101, 0.88901301616377926, 131.02661645825034},
      {8102, 0.79986196932364972, 131.70193679394416},
      {8103, 0.81784207742617943, 132.33926666580987},
      {8104, 0.81115855467691789, 132.25147476512998},
      {8105, 0.81695584308363112, 133.84081532984615},
      {8106, 0.79665759362220878, 134.39587965402461},
      {8107, 0.81402365871592774, 134.68237607474714},
      {8108, 0.82002218810872174, 135.1778457504916},
      {8109, 0.78010036249177617, 136.03386497705921},
      {8110, 0.79401695068305833, 136.32658175789433},
      {8111, 0.81448548097885676, 136.36358261897723},
      {8112, 0.86017750486977385, 137.82500738989063},
      {8113, 0.85885266837807506, 137.89431813800459},
      {8114, 0.81347411602316855, 138.32064414142323},
      {8115, 0.8547491582708755, 139.57413666799471},
      {8116, 0.838858860408416, 140.26734696500404},
      {8117, 0.82493969220449181, 141.16873369404567},
      {8118, 0.83761658432126318, 141.0812887969258},
      {8119, 0.8473999922599621, 142.57864771427469},
      {8120, 0.85728144067905931, 143.05704995566066},
      {8121, 0.85288251912434376, 143.60297651942577},
      {8122, 0.83484049071840449, 144.62790936781093},
      {8123, 0.84194842554728522, 144.81849143415286},
      {8124, 0.85282059882093419, 145.13420041383387},
      {8125, 0.8757569112088649, 146.53483530182885},
      {8126, 0.87268282614584813, 146.405621457672},
      {8127, 0.86654884608934579, 147.44039892557416},
      {8128, 0.89331002721913333, 148.42340860311788},
      {8129, 0.92462364065583924, 149.23738899099075},
      {8130, 0.84645183761400433, 149.66187716073975},
      {8131, 0.87601749248571315, 150.77613129586553},
      {8132, 0.92704885253937741, 151.92531712269789},
      {8133, 0.88451605412866519, 152.4621958899356},
      {8134, 0.91649531082702307, 153.614633268645},
      {8135, 0.908535971826262, 154.84595612332762},
      {8136, 0.94281917981398111, 155.47143646621856},
      {8137, 0.88271004527922192, 155.68481795165084},
      {8138, 0.89711038584089065, 157.12860980092276},
      {8139, 0.877510029799146, 157.70093433921525},
      {8140, 0.92030856951199058, 158.38735878882906},
      {8141, 0.88767269959622808, 159.61829608400058},
      {8142, 0.89185490008901047, 160.25987996247221},
      {8143, 0.90880042312207332, 160.87169864668613},
      {8144, 0.89719939627704171, 162.69944350910563},
      {8145, 0.9198983475019028, 163.40878304566309},
      {8146, 0.8850217366065094, 164.51077638833553},
      {8147, 0.892876585095267, 165.93121618321788},
      {8148, 0.90743043640913845, 166.15562467066792},
      {8149, 0.90557669732581692, 167.57332699302137},
      {8150, 0.90571988802745129, 168.43620917888677},
      {8151, 0.89444652278796166, 169.44469148813118},
      {8152, 0.91535494523923167, 171.71831022118263},
      {8153, 0.91029296043550612, 171.78457504915883},
      {8154, 0.90541157651672488, 171.92880001028158},
      {8155, 0.9212347940504908, 173.936241308846},
      {8156, 0.91189385827990554, 175.55816165225102},
      {8157, 0.91253241140881591, 176.16489095091828},
      {8158, 0.85812510481301363, 176.85509388374095},
      {8159, 0.8931320063468311, 178.46021668444524},
      {8160, 0.948020485300378, 179.9581282370934},
      {8161, 0.94680658935228779, 181.0352401393155},
      {8162, 0.88157999974199874, 182.3470549679343},
      {8163, 0.95084043911815164, 183.31162204886323},
      {8164, 0.92810149769733874, 184.64642907632793},
      {8165, 0.88319250764328749, 186.14362091788868},
      {8166, 0.90503360466466287, 186.77440913004924},
      {8167, 0.90422348069505543, 188.58993175596655},
      {8168, 0.92509965298829966, 189.97185415568893},
      {8169, 0.93291451128110525, 191.99813646236296},
      {8170, 0.90751299681368436, 193.42110809803492},
      {8171, 0.91644500058050282, 194.09338251359097},
      {8172, 0.92535894425882692, 196.17495405415826},
      {8173, 0.92295953250170926, 197.12720893469907},
      {8174, 0.92580141642694047, 199.55055327789844},
      {8175, 0.91115210464531271, 200.21685152103228},
      {8176, 6.8720520130548639, 443.26570191109},
      {8177, 0.93521459255150352, 204.3933992211698},
      {8178, 0.91570324694591, 204.78328985078846},
      {8179, 0.89274500445052185, 206.14410929326942},
      {8180, 0.9216011558456636, 207.60906835970133},
      {8181, 0.91689779279918471, 208.98353660887557},
      {8182, 0.91359537661734547, 211.0648896657199},
      {8183, 0.91056386176292259, 212.13734914984127},
      {8184, 0.94285658999729094, 216.08184143222508},
      {8185, 0.92694307202105286, 215.59815702553689},
      {8186, 0.91459513151614447, 217.88086211106685},
      {8187, 0.92734942401217768, 219.37849092007352},
      {8188, 0.90578309833718185, 221.18781888984566},
      {8189, 0.9409061004398922, 222.4230487475742},
      {8190, 0.90039861195319859, 224.21321440964414},
      {8191, 0.91722674441104757, 226.16013571694791},
      {8192, 21363.651017169985, 1440133.0411906077},
      {8193, 1.8905120035088172, 229.18757470215527},
      {8194, 1.6591080896296393, 230.58417406726727},
      {8195, 1.7107289825720147, 232.15187189142645},
      {8196, 1.6867916252789639, 233.98969270906966},
      {8197, 1.6856499696848515, 236.00556490894368},
      {8198, 1.6799055715373006, 238.13756763356423},
      {8199, 1.6889652859299011, 238.74722718451594},
      {8200, 6.48078148582928, 250.09229009497616},
      {8201, 1.6837046401527367, 243.24911000012852},
      {8202, 1.710083979411499, 244.71516148517523},
      {8203, 1.6915685186857417, 246.88742947473943},
      {8204, 1.7323146583418259, 247.75878111786554},
      {8205, 1.7128600730143577, 250.13055045046204},
      {8206, 1.6818650911389466, 251.40179156652829},
      {8207, 1.6369741611733897, 253.94882340089194},
      {8208, 1.89871128368529, 261.99491061445332},
      {8209, 1.5458674647505772, 257.59724453469391},
      {8210, 1.493084276112953, 258.18256242851083},
      {8211, 1.4907751647983074, 260.24476602963665},
      {8212, 1.5076381274268245, 262.17710033543676},
      {8213, 1.4924315329145112, 263.420889614312},
      {8214, 1.4623795456597737, 264.77156884165072},
      {8215, 1.475173828351759, 266.41087791900679},
      {8216, 1.47921670816187, 268.30925728386177},
      {8217, 1.4665230459629253, 267.4973974733},
      {8218, 1.4282962886518145, 269.26798956418924},
      {8219, 1.3874637185722209, 270.91687336940458},
      {8220, 1.3845315342045177, 273.071868292871},
      {8221, 1.3765463950773358, 273.578981865851},
      {8222, 1.3620196338962061, 275.42772686964236},
      {8223, 1.3530811800977824, 275.9783444074593},
      {9216, 184.90269482320457, 2538.1366936986724},
      {9704, 48.242661799042843, 128.70797722628487},
      {10240, 54.471005817928521, 198.81419887159589},
      {12288, 232.03628013777256, 169.39573828220378},
      {15361, 203.28471729511477, 156.83528897685355},
      {16070, 44.901726028457539, 27.908866583557174},
      {16384, 244.95637585624166, 108921.26851649556},
      {16392, 2.2884376733445992, 5.1079695150946547},
      {20480, 243.13550097395472, 214.9136860774461},
      {24576, 145.60393838929815, 135.14714236142351},
      {30000, 147.07904384731475, 144.93124188718525},
      {30488, 20.522653801003614, 11.034122016733285},
      {30721, 6.8533314413240651, 16.227107404027812},
      {32768, 524.922363549581, 4679.407459291343},
      {32776, 1.1706446161586193, 0.69653896078859778},
      {32784, 44.817443465472984, 1.3515274582631829},
      {36864, 86.319030173247825, 63.289041113495891},
      {40960, 63.481839291012541, 144.77890732434545},
      {45056, 54.199369186909024, 52.800382989114382},
      {49152, 61.9374166333415, 77.443046434217123},
      {49208, 0.863477341038971, 22.63502936678276},
      {49216, 2.2756550007095031, 0.177820046524181},
      {53248, 57.368237464363581, 45.079001143826552},
      {57344, 58.293655748913181, 56.5405929905281},
      {61440, 60.002017569886071, 39.4813967535889},
      {61441, 0.56191901340316563, 0.0084309013096171385},
      {65536, 3308.2954295076042, 1892.4885681604958},
      {65544, 6.21801751828584, 1.4995694585459265},
      {65552, 51.97892774674596, 0.11186366615687131},
      {67026, 24.89337323752887, 2.6211235204153769},
      {69632, 28.639920535610628, 4.422997339639374},
      {73728, 36.610247810214283, 17.944839285943804},
      {76490, 114.48405294185937, 4.3497924404631858},
      {76590, 47.1730104877514, 0.54829132876659536},
      {76606, 32.969675821411535, 0.0473467079643743},
      {77824, 6.8280782775835576, 1.5227415851636703},
      {81920, 304.33766044453625, 17.184914341528611},
      {86016, 22.705309666017385, 5.5502319783058507},
      {90112, 30.052787058656584, 12.481383901605211},
      {98304, 61.64898412002217, 18.6104049660065},
      {102415, 24.040259807273049, 12.277859887673662},
      {104864, 16.100813993988567, 2.2983330977136309},
      {122881, 69.282713915298189, 32.760927399144052},
      {131072, 128.34487931990861, 64.197432173656011},
      {131088, 5.7047240031476143, 0.10839363055687645},
      {135168, 14.688785975051276, 3.6458121811101551},
      {139264, 12.404197680568634, 5.6374069837679484},
      {196608, 100.63287839110414, 56.789510210901149},
      {196615, 1.3702395541738153, 0.069439267951008243},
      {196744, 0.16114371960422605, 6.1621406264056811},
      {262140, 55.174457874843576, 33.315092084463259},
      {262144, 26.317540215947059, 1027.4488041229165},
      {262160, 0.76209187425018388, 0.069169376293230833},
      {327687, 19.422585430668615, 12.03292678224887},
      {393216, 8.4620106038519562, 12.132311172229448},
      {403000, 0.63678324023787725, 2.0263337146088496},
      {524288, 8.45077851881474, 38.832217352748479},
      {524304, 0.36571292199331779, 0.049107429731779083},
      {589831, 1.2836182097292277, 2.7360459586937376},
      {655360, 1.101683458248945, 2.0627690884087944},
      {786432, 1.7334795340497156, 3.8464316467246724},
      {917504, 0.73106464221674616, 4.2969450834736413},
      {983040, 0.90511100504392483, 2.4635967561593142},
      {1048576, 1.3088223532295302, 90.091390456116528},
      {1048584, 0.0018318089758639815, 0.86798442339575121},
      {1048592, 0.60471239309072611, 0.050508295955480724},
      {1081344, 0.7070215044053717, 0.56406071277101577},
      {1114119, 0.083315058243785378, 0.368067961289825},
      {1179648, 0.12251319031463255, 0.52265162127774378},
      {1572864, 0.25210593531908293, 2.8560063745839144},
      {2097152, 0.59274629445684313, 2.5706152244598948},
      {2097160, 2.5800126420619463e-06, 0.97930830623706766},
      {2129920, 1.1680400933964576, 0.3313241398809908},
      {3145728, 1.7855506391981322, 1.3281625518898839},
      {3670024, 0.02975141578193732, 0.44987083756377816},
      {4194304, 0.35975309279015488, 0.34836587027207688},
      {8388608, 0.078200183180897581, 11.632304746237574},
      {16777216, 0.015876107792928185, 4.5469033145265971},
      {16842752, 0.40803544937370195, 0.006683031525916025},
      {33619968, 0.0067467330589919888, 0.0076983382385071141},
  };
  return e;
}

EmpiricalProfile Charlie() {
  static constexpr EmpiricalData::Entry e[] = {
      {1, 10029.032862491491, 9379.8439414567729},
      {2, 313.40869639210348, 1817.9669843430906},
      {3, 482.93941456773314, 5420.4414567733156},
      {4, 371856.47351940093, 31373.88070115725},
      {5, 6306.0900612661671, 15313.321307011573},
      {6, 3925.9713580667121, 1182.2360449285229},
      {7, 3480.9535738597688, 613.42409802586792},
      {8, 793406.7814159292, 133425.54050374404},
      {9, 703.785908781484, 312.28863172226005},
      {10, 1020.5448944860449, 312.28863172226005},
      {11, 1240.2684309053777, 206.33356024506466},
      {12, 49749.6225493533, 9692.1485704560928},
      {13, 1615.5823349217155, 1695.2823349217153},
      {14, 1881.0343601089176, 948.01940095302928},
      {15, 3091.1812968005447, 395.93737236215111},
      {16, 489190.73824029951, 337318.15486725664},
      {17, 89485.0222940776, 26288.054458815521},
      {18, 50644.380922396187, 52821.586113002042},
      {19, 35080.068805309733, 68729.017188563652},
      {20, 62715.527842069438, 78390.60857726344},
      {21, 42831.806211708645, 13110.62729748128},
      {22, 29636.32731449966, 12789.952518720218},
      {23, 6386.3382573179033, 22780.624404356706},
      {24, 123131.02442137508, 239690.066712049},
      {25, 37202.230479918311, 3638.7219196732472},
      {26, 13120.001820966643, 6089.6351259360108},
      {27, 4704.3380360789652, 10394.770592239618},
      {28, 19890.658577263446, 51274.364193328794},
      {29, 3184.3915248468347, 7034.8687882913546},
      {30, 1726.6020762423418, 13110.602620830497},
      {31, 369529.98710006807, 252687.452688904},
      {32, 826440.0278590878, 1811431.8628318585},
      {33, 21046.595098706603, 8694.1674608577268},
      {34, 5276.8684479237572, 3307.0144656228726},
      {35, 4280.8525527569773, 4074.7474472430226},
      {36, 23820.847532334923, 3059.7785908781484},
      {37, 7417.2984853641938, 4184.4235874744727},
      {38, 4846.517767188564, 2983.5627978216476},
      {39, 3443.1143464942138, 3946.4833219877469},
      {40, 708769.36955411849, 690371.952688904},
      {41, 7438.8307351940093, 4569.2197072838662},
      {42, 6013.8292886317222, 3043.0515656909461},
      {43, 3538.6475323349218, 4896.3892103471753},
      {44, 60635.24651123213, 3563.5450987066033},
      {45, 4449.5526378488767, 3347.9106535057863},
      {46, 6252.3578284547311, 2000.1957113682777},
      {47, 3888.7106875425461, 3953.9178012253233},
      {48, 606985.71518039482, 416527.635125936},
      {49, 17860.202791014297, 26054.891933287952},
      {50, 2424.4860279101431, 6266.84768550034},
      {51, 2256.0980769230769, 4174.132573179033},
      {52, 22664.708645336963, 2197.1902654867258},
      {53, 1493.1371341048332, 2105.1650782845472},
      {54, 2096.5906398910824, 1976.9205241660993},
      {55, 9386.7646528250516, 2825.955241660994},
      {56, 71580.134053778078, 162328.60959836622},
      {57, 4415.4032505105515, 4677.4290333560248},
      {58, 1181.0925289312459, 6291.9962559564328},
      {59, 1587.6716303607895, 1675.7680394826411},
      {60, 7216.9117086453371, 1140.4188223281144},
      {61, 4075.1833219877467, 5851.2802927161338},
      {62, 896.80209326072156, 15630.087644656229},
      {63, 1442.804441797141, 8179.5818584070794},
      {64, 353577.91104492854, 406285.91439754935},
      {65, 14469.850970047652, 10924.089516678012},
      {66, 1736.7189244383935, 7782.0384615384619},
      {67, 1260.5208645336963, 1267.0769230769231},
      {68, 22235.983832539143, 718.30769230769226},
      {69, 1246.4572838665758, 1153.3083730428864},
      {70, 1089.501038121171, 572.19230769230774},
      {71, 888.49673247106875, 1059.6153846153845},
      {72, 276340.90362491494, 296995.96936691628},
      {73, 1193.2437542545949, 1064.0774336283187},
      {74, 1136.2593430905379, 600.07692307692309},
      {75, 997.59583049693674, 944.73076923076928},
      {76, 1185.227620830497, 527.57692307692309},
      {77, 1707.4883934649422, 813.11538461538464},
      {78, 901.54652825051051, 421.61538461538464},
      {79, 2593.7799863852961, 754},
      {80, 148859.16657590197, 239738.84172906738},
      {81, 945.80767528931244, 898.70847515316541},
      {82, 815.02161334240975, 454.46630360789652},
      {83, 1315.1093601089176, 468.41150442477874},
      {84, 1507.0643975493533, 334.5770932607216},
      {85, 2289.9103982300885, 513.94605173587479},
      {86, 1375.3443839346494, 308.55769230769232},
      {87, 2225.3150272294079, 439.59700476514638},
      {88, 300048.83296460175, 81386.8061606535},
      {89, 1297.4491320626275, 468.40759019741319},
      {90, 2007.4339176310416, 255.58032675289311},
      {91, 3851.33861470388, 1183.1186181075561},
      {92, 2516.1571477195371, 1291.8473451327434},
      {93, 2272.9852961198094, 468.40724982981618},
      {94, 1063.3932947583389, 249.07420013614703},
      {95, 1566.5512933968687, 375.46817562968005},
      {96, 195541.25866235534, 532322.71375085087},
      {97, 1554.9180224642614, 850.01123213070116},
      {98, 1816.8979067392784, 703.42937372362155},
      {99, 1827.7982130701157, 940.03318584070792},
      {100, 5038.7149421375088, 6859.1902654867254},
      {101, 1426.1516507828455, 914.536929884275},
      {102, 1404.1714091218516, 736.89091218516},
      {103, 1971.8044928522804, 740.07794417971411},
      {104, 45464.036215112319, 56004.096494213751},
      {105, 1437.0702178352622, 701.04050374404358},
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      {449, 365.6528080326753, 183.80582028590879},
      {451, 395.86461878829135, 351.820115724983},
      {452, 213.16289993192649, 191.43550034036761},
      {453, 190.16870319945542, 177.30445881552077},
      {454, 357.38633424098026, 177.67358747447244},
      {455, 830.14419673247107, 165.59479237576582},
      {456, 142.9028080326753, 215.96204901293396},
      {457, 267.83628318584073, 175.6286589516678},
      {458, 174.74930224642614, 171.91524846834582},
      {459, 188.18424098025869, 167.822157930565},
      {460, 208.97785908781483, 183.06705241660993},
      {461, 222.88893805309735, 170.61351259360109},
      {462, 161.96848196051735, 168.56671204901292},
      {463, 225.83866575901973, 174.51616746085773},
      {464, 2761.4826242341728, 208.34104833219877},
      {465, 209.19802586793736, 177.11742682096664},
      {467, 549.30913886997962, 333.41933287950985},
      {469, 421.59508168822327, 326.91354663036077},
      {471, 390.68915929203536, 332.11504424778764},
      {472, 403.26186181075559, 13413.255786249149},
      {475, 443.92581688223282, 516.6659292035398},
      {477, 291.61604833219877, 336.02195371000681},
      {480, 3762.9779441797141, 1794.215452688904},
      {481, 1411.7338155207624, 202.52654867256638},
      {483, 233.11992852280463, 338.10142954390744},
      {487, 375.19475833900611, 657.37882913546628},
      {488, 330.88117767188561, 920.30888359428184},
      {489, 201.09123553437712, 174.80292716133425},
      {491, 540.7260721579305, 319.45166780122531},
      {494, 355.622617426821, 501.05003403675971},
      {504, 1479.4581518039483, 2197.3245405037442},
      {511, 778.29150782845477, 1089.5856024506468},
      {512, 41035.054833219874, 142841.27825051054},
      {515, 492.43686181075566, 475.78641933287952},
      {516, 154.25231449965963, 149.92392784206945},
      {517, 175.23861470388019, 154.72447243022464},
      {518, 180.48847855684139, 146.35925799863853},
      {519, 227.94317562968004, 149.30122532334923},
      {520, 8643.5493703199463, 706.75663716814154},
      {523, 530.12389380530976, 448.99098025867943},
      {528, 544.512729748128, 814.969537100068},
      {535, 680.43066712049017, 970.00187202178358},
      {536, 5252.9292545949629, 177.49081007488087},
      {539, 280.82646358066711, 415.69196732471062},
      {544, 503.04081007488082, 691.37389380530976},
      {547, 333.55194009530294, 445.89244383934647},
      {550, 208.83243703199457, 441.55428863172227},
      {552, 151.08075221238937, 1144.8146698434309},
      {560, 2239.2868447923756, 1276.8000340367598},
      {576, 8937.4253233492182, 87896.296119809384},
      {584, 1889.7699795779442, 26544.88750850919},
      {592, 5173.5998127978219, 1091.3390061266168},
      {597, 235.09834921715455, 558.817392784207},
      {600, 2051.667171545269, 382.35074880871343},
      {608, 112.932726344452, 901.85568413887006},
      {616, 1834.3532675289312, 1055.7489788972091},
      {624, 129.96841388699798, 907.57709326072165},
      {632, 557.73934649421381, 881.789993192648},
      {640, 6220.9883253914213, 20947.740299523488},
      {656, 941.84792375765824, 1718.5970047651465},
      {664, 397.00108917631036, 826.2704220558204},
      {672, 425.86135125936011, 1548.833049693669},
      {680, 348.78648740639892, 728.6444860449285},
      {696, 714.91502722940777, 2421.507147719537},
      {704, 682.59365214431591, 5704.1255956432951},
      {720, 525.519213750851, 1725.7590197413206},
      {752, 626.15592239618786, 2106.0723281143637},
      {760, 475.81349557522122, 454.36470388019063},
      {768, 5253.0089006126618, 13419.712219196734},
      {776, 6009.8495915588837, 552.79850238257325},
      {777, 100.60827093260721, 49.684138869979577},
      {792, 142.69700476514635, 976.15418652144331},
      {800, 844.03395166780115, 542.50527569775352},
      {816, 185.10321647379169, 1588.0604152484682},
      {824, 171.69993192648059, 351.56211708645344},
      {832, 99.5041014295439, 21319.321647379169},
      {840, 193.11562287270252, 352.75323349217155},
      {864, 3845.3184479237575, 974.62831858407083},
      {880, 196.66033015656913, 488.95609257998643},
      {960, 647.5435500340368, 2725.0391422736552},
      {961, 219.21800544588154, 28.755956432947585},
      {968, 95.064857045609244, 574.491150442478},
      {1000, 1900.2349046970726, 1302.9790673927844},
      {1008, 31.15217835262083, 1738.53863172226},
      {1016, 1062.98180735194, 189.61589516678012},
      {1024, 12544.092273655548, 8760.055650102111},
      {1032, 29.212848876786932, 482.10704560925797},
      {1040, 305.843294758339, 410.96902654867256},
      {1048, 1092.2526889040164, 13995.177161334241},
      {1056, 3004.8601259360107, 180.43618107556165},
      {1072, 974.2027910142956, 344.14363512593604},
      {1088, 2582.0879680054459, 7258.2008168822322},
      {1104, 107.57729748127979, 15288.179884275016},
      {1112, 1766.9818413886999, 158.76514635806674},
      {1128, 413.73728727025184, 273.59309053778082},
      {1144, 213.95377808032674, 312.500340367597},
      {1152, 6638.4087814840032, 3659.3502382573179},
      {1176, 371.76695030633084, 1074.3311776718858},
      {1184, 69.522855684138875, 129.712389380531},
      {1272, 1208.1146868618112, 1469.7503403675971},
      {1280, 2017.7422906739278, 2387.7780803267533},
      {1296, 67.761623553437715, 816.61810755616057},
      {1320, 198.33861470388018, 372.47974812797821},
      {1336, 61.538869979577953, 415.52876106194691},
      {1408, 548.00719877467679, 3824.5685840707956},
      {1416, 180.00348876786933, 125.02637848876788},
      {1424, 483.82826752893129, 121.07692307692309},
      {1440, 291.44702178352622, 948.63410483321979},
      {1448, 286.82857385976854, 122.93890401633763},
      {1504, 339.92062627637853, 779.110789652825},
      {1536, 809.27646358066727, 5142.0359087814832},
      {1544, 55270.621494213752, 13410.724472430224},
      {1584, 50.155343771272968, 652.62899931926484},
      {1592, 27.684394145677338, 172.22974812797821},
      {1616, 22.146187882913544, 374.87644656228736},
      {1632, 13.400595643294755, 263.08543226684816},
      {1696, 192.7361810755616, 903.58287950987051},
      {1728, 1255.1995405037437, 761.00646698434286},
      {1792, 136.07828454731109, 919.831688223281},
      {1872, 106.64339686861811, 2389.8849557522112},
      {1920, 101.28155207624233, 853.98110959836617},
      {1928, 32.919503063308376, 375.5951327433628},
      {2016, 103.66594622191967, 1576.8594281824373},
      {2048, 728.65684138869983, 10559.150272294077},
      {2070, 112.23202859087817, 243.60057862491493},
      {2080, 53.271630360789651, 112.75833900612662},
      {2112, 30.743550034036772, 379.0559904697073},
      {2160, 31.830428863172219, 572.4058883594281},
      {2304, 575.3069605173589, 3348.5061266167463},
      {2400, 187.66953710006803, 872.18243703199448},
      {2430, 106.15353982300884, 219.26923076923077},
      {2448, 23.238087134104838, 1018.3010551395506},
      {2536, 78.242733151803932, 984.24846834581342},
      {2560, 260.73148400272294, 3820.0406739278424},
      {2592, 23.3644996596324, 414.56807351940091},
      {2736, 89.721851599727728, 333.92494894486038},
      {2816, 2132.1451837985028, 1727.0884955752213},
      {2880, 25.881875425459498, 143.79033356024505},
      {3024, 24.035738597685498, 255.10364193328795},
      {3072, 263.42384275017014, 3904.0173587474492},
      {3112, 8.5679203539822986, 142.83458134785567},
      {3168, 6.8987406398910833, 2152.9409462219196},
      {3328, 86.004901293396841, 301.48008849557527},
      {3360, 4.3683117767188575, 71.725153165418646},
      {3456, 16.8751021102791, 168.22260040844117},
      {3520, 8.7953199455411841, 780.76786929884258},
      {3600, 11.796102791014297, 266.79782164737918},
      {3607, 0.75285908781484, 56.68430905377808},
      {3744, 28.679543907420019, 208.51752893124572},
      {3840, 14.220847515316544, 1049.209666439755},
      {4096, 2236.3876106194689, 1424.4445200816876},
      {4136, 31.167137508509185, 46.718345813478564},
      {4224, 5.8369298842750181, 126.81041524846836},
      {4608, 21.938597685500326, 3041.3842750170188},
      {4800, 9.8897379169503079, 221.76140231449969},
      {5224, 31.864108236895866, 505.15588835942822},
      {5632, 113.56078965282508, 1825.9663036078962},
      {5760, 5.0869979577944218, 150.96766507828457},
      {6144, 123.59314159292036, 3635.2329816201486},
      {6152, 1.7680565010211027, 64.862491490810086},
      {6192, 1.587593601089176, 194.93550034036758},
      {6365, 3.9909972770592237, 315.30667120490125},
      {6366, 0.016337644656228726, 100.68703199455412},
      {6400, 1.6336963921034717, 91.233151803948289},
      {6401, 0.023144996596324029, 40.4712389380531},
      {6470, 2.1078795098706609, 121.89635806671205},
      {6471, 0.049012933968686181, 24.456262763784888},
      {6720, 8.4781994554118416, 430.60704560925808},
      {6912, 4.55987066031314, 362.00799863852956},
      {7680, 22.217631041524839, 2412.039312457453},
      {8000, 7.9637848876786945, 1966.6742682096658},
      {8184, 8.0731960517358718, 1567.4508168822331},
      {8192, 26456.968839346493, 1239110.3151803948},
      {8195, 0.12916950306330838, 28.943669162695709},
      {8200, 0.23259019741320627, 52.95966643975494},
      {8205, 0.2011061946902655, 48.968175629680054},
      {8208, 0.17047311095983664, 33.100408441116407},
      {8211, 0.12511912865895167, 29.553267528931244},
      {8215, 0.16858407079646018, 39.802416609938732},
      {8216, 0.058151803948264122, 13.201497617426821},
      {8217, 0.052212389380530973, 10.243362831858407},
      {8220, 0.13498978897208985, 29.907420013614704},
      {8222, 0.069060585432266855, 20.052927161334239},
      {8224, 0.076940095302927169, 20.022123893805308},
      {8229, 0.20978556841388699, 49.682096664397548},
      {8230, 0.038461538461538464, 10.343260721579306},
      {8231, 0.040418652144315864, 10.129169503063308},
      {8233, 0.090673927842069429, 20.294758339006126},
      {8235, 0.073944860449285221, 20.39516678012253},
      {8236, 0.037440435670524165, 10.168481960517358},
      {8237, 0.053199455411844794, 10.081688223281144},
      {8240, 0.12906739278420695, 29.76293396868618},
      {8241, 0.03156909462219197, 10.52791014295439},
      {8243, 0.068975493533015658, 19.866405718175628},
      {8244, 0.0423927842069435, 10.517699115044248},
      {8245, 0.027603812117086454, 10.246936691626956},
      {8246, 0.027620830496936692, 10.136827773995915},
      {8247, 0.041405718175629679, 10.548162014976175},
      {8408, 49.16346153846154, 32.549183117767186},
      {8448, 2.5828454731109574, 15.898059904697076},
      {9704, 13.1215452688904, 143.75901974132066},
      {9936, 2.8540503744043564, 35.516167460857716},
      {9984, 1.1406398910823687, 15.809053778080328},
      {10072, 0.41725663716814154, 137.91218515997284},
      {11264, 68.949761742682085, 251.78948264125256},
      {12288, 26.100238257317898, 552.15571817562977},
      {12344, 1.1502552756977538, 25.175799863852962},
      {12816, 1.5768209666439761, 35.087474472430223},
      {12960, 0.35194009530292719, 16.666609938733835},
      {13008, 0.10891763104152485, 8.9535398230088461},
      {13056, 0.30345473110959831, 16.519571136827778},
      {13824, 4.5012593601089179, 52.937712729748128},
      {13928, 0.34531994554118439, 9.5311436351259342},
      {16373, 9.590129339686861, 43.947923757658252},
      {16384, 91.762474472430227, 43879.906398910811},
      {16392, 0.024285228046289995, 5.0353982300884956},
      {16896, 2.9872532334921731, 102.66592920353985},
      {16983, 0.059632402995234868, 8.75238257317903},
      {18440, 2.9250510551395505, 29.27484683458135},
      {19200, 1.477876106194691, 13.815520762423407},
      {19968, 2.2864193328795106, 25.304969366916268},
      {22528, 48.956518039482653, 187.42358747447241},
      {24576, 15.586181075561605, 172.62882913546619},
      {24632, 0.26507828454731119, 11.943669162695713},
      {29912, 9.054322668481964, 61.703369639210344},
      {30488, 5.1998808713410494, 5.1060245064669862},
      {30523, 0.010976855003403674, 9.793567052416611},
      {32768, 357.48808713410369, 91.44741320626278},
      {33024, 0.18618107556160648, 14.471409121851602},
      {33792, 2.0395336963921049, 6.0267188563648721},
      {36872, 1.7586283185840712, 24.666609938733835},
      {38912, 0.97619128658951682, 11.114193328795102},
      {45056, 26.731535057862487, 77.81960517358749},
      {45064, 0.0030633083730428863, 2.7331518039482638},
      {49152, 6.803556841388696, 63.506126616746094},
      {49208, 0.090929203539823, 14.230939414567732},
      {60136, 3.1151974132062632, 39.16678012253233},
      {65536, 9884.9547311095939, 150.61742682096673},
      {74256, 1.0434819605173589, 26.620830496936684},
      {76490, 22.062968005445907, 3.7733151803948246},
      {81920, 286.61356364873967, 11.189244383934648},
      {90112, 11.848893805309741, 36.52297481279782},
      {98304, 1.4553097345132737, 9.4790673927842057},
      {98312, 0.022038801906058544, 6.4269911504424782},
      {108240, 0.46952008168822307, 12.070966643975492},
      {108768, 0.018822328114363508, 4.0890061266167486},
      {109296, 0.029731109598366223, 6.9773655547991886},
      {109824, 0.03039482641252552, 7.625085091899253},
      {109872, 0.0032675289312457455, 0.81330837304288639},
      {116320, 0.13725323349217153, 9.1369979577944189},
      {121384, 0.084445200816882213, 5.3046289993192657},
      {131072, 0.73660653505786233, 47.474472430224658},
      {131073, 0.011300204220558203, 36.870490129339686},
      {140448, 0.30115724982981612, 7.2071136827774005},
      {140976, 0.0099387338325391435, 1.9440095302927156},
      {141504, 0.010074880871341048, 1.3379850238257318},
      {142032, 0.0089857045609258, 1.6693328795098707},
      {142560, 0.0095302927161334226, 2.7479577944179727},
      {143088, 0.010840707964601773, 3.0970047651463584},
      {147456, 0.086504424778761038, 3.291184479237578},
      {152064, 0.068924438393464946, 2.1220217835262076},
      {159744, 0.11752893124574543, 4.33492171545269},
      {163840, 0.074438393464942132, 1.509870660313138},
      {180224, 7.7550544588155228, 52.344792375765834},
      {185856, 0.089414567733151845, 3.4434989788972077},
      {191520, 0.16766507828454738, 3.52501701837985},
      {192240, 0.023332198774676655, 3.8932947583390067},
      {192960, 0.0099387338325391435, 0.7486385296119813},
      {196744, 0.22311095983662346, 5.5644996596324061},
      {227176, 0.2192477876106195, 9.2294077603812141},
      {253440, 0.10418652144315856, 8.1283185840707954},
      {262144, 0.21485704560925808, 149.54203539823018},
      {299520, 0.067733151803948274, 7.5946221919673249},
      {327680, 0.054118447923757661, 3.111130020422058},
      {354816, 0.035023825731790352, 2.3567052416609924},
      {360448, 4.3070456092579992, 3.2108577263444524},
      {371712, 0.015044247787610619, 1.4853641933287953},
      {393256, 0.0996596324029952, 2.9208645336963923},
      {458760, 0.049234172906739267, 1.6727365554799183},
      {489984, 0.017562968005445882, 1.3677671885636489},
      {497864, 0.010755616065350589, 0.54373723621511227},
      {506880, 0.0099387338325391539, 1.3008849557522126},
      {524288, 0.11158951667801206, 8.0985364193328877},
      {720896, 2.6331858407079727, 2.7169843430905374},
      {786536, 0.038529611980939432, 1.3774676650782853},
      {917512, 0.039108236895847526, 1.20353982300885},
      {957696, 0.0096153846153846159, 0.50799863852961191},
      {990720, 0.011759700476514642, 0.87848876786929853},
      {1010168, 0.0034547311095983638, 0.31279782164737918},
      {1048576, 0.026463580667120554, 2.758509189925122},
      {1048584, 3.4036759700476515e-05, 0.8584070796460177},
      {1441792, 1.7970217835262103, 0.94860449285228055},
      {2050232, 0.043890401633764453, 0.72089857045609229},
      {2097152, 0.010398230088495585, 1.1426140231449968},
      {2883584, 0.44663036078965274, 0.40673927842069441},
      {3145728, 0.26072157930565032, 0.2452348536419332},
      {4194304, 0.021324029952348535, 0.59292035398230125},
      {5767168, 0.22477876106194675, 0.15265486725663713},
      {8388608, 0.064754935330156485, 4.8830837304288668},
      {11534336, 0.058373042886317138, 0.055820285908781436},
      {16777216, 0.0042886317222600454, 3.724302246426141},
      {23068672, 0.024063989108236903, 0.016507828454731113},
      {33554432, 0.000953029271613342, 0.15673927842069449},
      {46137344, 0.006228727025187209, 0.00918992511912866},
      {92274688, 0.0015827093260721576, 0.0045949625595643282},
  };
  return e;
}

EmpiricalProfile Echo() {
  static constexpr EmpiricalData::Entry e[] = {
      {1, 13.217131473633088, 998.0186499280419},
      {2, 0.41019351333956283, 85.682004705479045},
      {3, 0.17026900553717703, 135.73479457182094},
      {4, 68.513886991988727, 13751.650678376631},
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      {262045, 0.000301289744486811, 2.3320426448978261e-06},
      {262060, 0.00029919355910135647, 2.3320426448978261e-06},
      {262075, 0.00030875925015610674, 2.623547975510054e-06},
      {262081, 0.00030182117176763047, 2.3320426448978261e-06},
      {262091, 0.00031752780028962787, 2.3320426448978261e-06},
      {262124, 0.00034144202792650363, 2.3320426448978261e-06},
      {262140, 0.06740419916123061, 0.0002302892111836603},
      {262144, 0.0051616941311237764, 0.9662463062630795},
      {262145, 0.00058173573007036983, 2.3320426448978261e-06},
      {262159, 0.00038026574316414754, 0.10137972388032074},
      {262160, 0.00037935050729162513, 0.025694154356153635},
      {262188, 0.00047267504255108715, 2.3320426448978261e-06},
      {262194, 0.00047902264618309738, 2.3320426448978261e-06},
      {262201, 0.0004864626281145698, 2.3320426448978261e-06},
      {262215, 0.00048956262058601663, 0.00026293780821222987},
      {262231, 0.00051666541190780921, 2.3320426448978261e-06},
      {262262, 0.00053452727329090773, 2.3320426448978261e-06},
      {262272, 0.00027173648292568432, 2.623547975510054e-06},
      {327664, 4.9068452262330212e-05, 0.066394420121563547},
      {457160, 0.0013457510174618146, 0.022182389638268119},
      {524288, 0.053987667934711214, 0.045211310756634142},
      {589816, 0.00011168830018555677, 0.0014581096637223652},
      {630672, 0.00034846867752844979, 0.0027917465512733095},
      {655344, 1.6533293181049897e-06, 0.013455303050399235},
      {693040, 0.00018475955129823257, 0.0026611521631590314},
      {713120, 0.0015239858227010974, 3.0608059714283962e-05},
      {1040704, 0.00019060525138724657, 0.0054735955929058108},
      {1047648, 0.00025065653411984561, 0.0019577498003917246},
      {1048576, 0.69702199961323907, 0.64191543488660008},
      {1048577, 1.3610443136542858e-05, 0.0041845590209385365},
      {1644033, 0.0014643773960358476, 0.0032115142273549187},
      {2097152, 0.0038908743602575034, 0.075599866956967091},
      {2097160, 5.9047475646606762e-08, 0.90228945371609537},
      {2162695, 0.0034390135528718471, 0.0011625232584815664},
      {3932160, 7.631886227323923e-05, 0.034161218189116424},
      {4194304, 6.2796990350166281e-05, 0.00077569568475913955},
      {4194320, 2.1257091232778437e-06, 0.00078269181269383288},
      {4595677, 4.1333232952624737e-07, 0.0028550032080161634},
      {8388608, 1.92199533229705e-05, 0.0011814711049713607},
      {16842752, 0.0036765024999225, 0.00045183326244895375},
      {29388580, 7.0856970775928117e-07, 0.00062440441817139287},
      {33554432, 1.7714242693982029e-07, 0.0005363698083265},
      {33620032, 0.0006641364823352096, 5.8301066122445652e-07},
  };
  return e;
}

EmpiricalProfile Merced() {
  static constexpr EmpiricalData::Entry e[] = {
      {1, 14569.776757880152, 8226.8176705447986},
      {2, 1293.275520807561, 3725.1391405143177},
      {3, 4543.983205502499, 866.573219422144},
      {4, 68691.406190311245, 201562.99201476839},
      {5, 1924.9980850116285, 1102.9112608938308},
      {6, 18585.822772032261, 1249.2159447044176},
      {7, 7380.88782225741, 1429.2829605460868},
      {8, 584834.75403533084, 758161.507362727},
      {9, 1286.1468801029243, 1181.6906366719616},
      {10, 3134.6159631847195, 720.26857854290984},
      {11, 3646.3474986392202, 298.23620830292361},
      {12, 18684.380325597507, 99391.449877645646},
      {13, 10744.432812113415, 5784.6570214227449},
      {14, 8193.55778613489, 7489.6678401236422},
      {15, 4668.51177693107, 5396.38728373331},
      {16, 427529.74302043644, 1695715.2936933844},
      {17, 90155.742020881778, 105358.9976387756},
      {18, 68901.379128111235, 45329.093976731208},
      {19, 35215.873200059381, 77029.525694414624},
      {20, 71189.817130981246, 102739.74722019491},
      {21, 36591.80620020783, 83019.412527368739},
      {22, 34553.285694492552, 30473.550852187353},
      {23, 14582.775030926814, 34049.572875971324},
      {24, 247370.26828145876, 3673003.9744558451},
      {25, 11549.013053589984, 51496.389988408533},
      {26, 13268.084670196447, 35521.058043188939},
      {27, 12882.826488198327, 53752.857510840164},
      {28, 15850.412895244694, 376011.32284377282},
      {29, 10645.534499480429, 580046.92414029967},
      {30, 8512.34480676926, 26213.837418967072},
      {31, 340919.51529516553, 280367.3833769802},
      {32, 749028.30704141723, 3484928.927102563},
      {33, 20835.587881636893, 34447.264843515222},
      {34, 34159.545123459844, 31757.511441205512},
      {35, 12936.909317630758, 47809.755634740053},
      {36, 12141.529699638775, 75570.131498733521},
      {37, 7437.3326884061553, 27711.621989438889},
      {38, 13153.097798010787, 24941.210664148028},
      {39, 21039.241986243753, 38827.0249001846},
      {40, 399319.02609728341, 1427270.1288369896},
      {41, 7758.395323865604, 26301.09990125789},
      {42, 4396.5577119105346, 21636.22216975057},
      {43, 3086.4175268444751, 39436.624994633581},
      {44, 5232.1479390370623, 29744.878461340319},
      {45, 14474.690321144044, 28156.159618769587},
      {46, 3148.0398535306053, 19192.180483407032},
      {47, 4139.7209015785047, 31673.098570385951},
      {48, 525444.1601613143, 1981684.928691023},
      {49, 5345.002825473799, 18694.627956896922},
      {50, 2684.9933000148449, 16232.771819860043},
      {51, 1794.321609184027, 33180.188296913235},
      {52, 3371.0303330199417, 97849.688575967026},
      {53, 2444.6943886387253, 26547.243334907482},
      {54, 1815.2434311445395, 18767.780792512771},
      {55, 3452.1101984264437, 43557.983471429186},
      {56, 230514.71963481617, 1157542.6717898082},
      {57, 2165.3155326834581, 25776.330442622246},
      {58, 1971.0642683952694, 23057.035289571973},
      {59, 1016.6686723736949, 45554.179925299446},
      {60, 1645.8027858874759, 29564.775898338557},
      {61, 13660.999505170963, 34698.096938994546},
      {62, 1474.2481072789351, 24266.861374661916},
      {63, 2056.1956751942203, 41868.4290130082},
      {64, 347765.06967192836, 743949.63392435492},
      {65, 1497.8531149487851, 32757.575924097368},
      {66, 855.36286802909592, 25892.520971965827},
      {67, 1219.7388292344995, 34768.704074185378},
      {68, 1471.1308278489782, 52560.488558794488},
      {69, 2716.8007917264586, 33615.146696432406},
      {70, 1029.7027512494433, 20516.389258575538},
      {71, 922.03688455638576, 30398.697720345168},
      {72, 126290.03358899501, 138462.537543468},
      {73, 2070.6820426542631, 36484.962048684152},
      {74, 886.36249195902815, 16652.818529171855},
      {75, 910.87912316294717, 26889.638303352938},
      {76, 1459.1926220990647, 126547.93444382433},
      {77, 887.14107575832554, 58554.465504658052},
      {78, 868.59374536097778, 12801.63864680376},
      {79, 773.7681231134643, 20274.422616236636},
      {80, 185984.53789400763, 1024627.4229596874},
      {81, 868.78967786629721, 19801.714549435452},
      {82, 629.67376416448121, 34925.463486884473},
      {83, 1788.4864119946558, 16250.091701369511},
      {84, 1096.7625513385126, 14516.948825827501},
      {85, 1108.4370775397101, 16878.44794573477},
      {86, 509.25230342916524, 18281.475894045423},
      {87, 683.61537928645657, 15729.58463916198},
      {88, 77713.74316888515, 955183.26711887692},
      {89, 388.83142659211245, 8292.4473876271841},
      {90, 355.86203671631449, 14709.211479843731},
      {91, 826.95948339848587, 16048.457004250204},
      {92, 1789.340580929289, 5703.05276263255},
      {93, 1058.6057202236627, 7102.3199244408188},
      {94, 358.77887080013858, 14276.866912806423},
      {95, 503.62976891483993, 13274.30270896836},
      {96, 143564.44323321292, 97873.370969819254},
      {97, 550.1128061754664, 4439.7933713991324},
      {98, 405.37669355237767, 6687.4180655132441},
      {99, 392.58947993468257, 17358.023912763492},
      {100, 913.03163936859812, 63443.223371828448},
      {101, 320.96574793408877, 3632.7043747048469},
      {102, 271.02389529417587, 5093.3379985403344},
      {103, 381.19275570290466, 14146.550637530589},
      {104, 124113.433282201, 140136.99510582577},
      {105, 470.6019050917908, 3470.3212553127551},
      {106, 255.45546538670888, 2659.2122096767271},
      {107, 255.1769904497996, 12570.961232988451},
      {108, 386.010094512346, 6802.3700682608505},
      {109, 269.07558018704538, 3099.7370025329496},
      {110, 198.10119748626849, 1966.2738161679474},
      {111, 252.39944579147905, 8811.2490018460485},
      {112, 53703.381641842745, 78738.652728287474},
      {113, 358.918308674353, 3956.5535139312242},
      {114, 195.22737394230293, 9488.0074700553814},
      {115, 222.06220495818695, 6049.8360880951359},
      {116, 361.43224800831314, 7938.43429356459},
      {117, 253.36018605571775, 5307.0590306100548},
      {118, 1299.1371814538077, 1255.546301463959},
      {119, 370.840853085259, 5148.7957326235346},
      {120, 24211.235345638081, 75253.610741424462},
      {121, 4097.2195061606217, 4656.4256214313309},
      {122, 239.33192636943937, 782.87008972652723},
      {123, 179.33762679994061, 3386.1072425192119},
      {124, 154.68959374536098, 3138.5167646932555},
      {125, 150.71697758424463, 4437.6714892886275},
      {126, 111.96369934187739, 11178.950671875671},
      {127, 139.28634766688108, 3757.4957283303997},
      {128, 99799.984927507539, 67622.3282101919},
      {129, 125.1080459201346, 4222.8400807109429},
      {130, 87.273313870057891, 3065.5279268449749},
      {131, 340.726874164976, 2514.6978062078738},
      {132, 2566.7041813053588, 15900.356630747436},
      {133, 176.27561977336831, 2717.2740308247112},
      {134, 1202.6287149289919, 4012.7594556304471},
      {135, 90.3718442278193, 4343.50938050058},
      {136, 33839.932238111731, 44808.321255312752},
      {137, 1767.259201345935, 2866.7048469497272},
      {138, 149.1789202830422, 3211.8339415274977},
      {139, 102.76792518184968, 4939.9844588502983},
      {140, 336.4760255331783, 1348.0102176619584},
      {141, 103.41544856252165, 3253.7302193792125},
      {142, 124.45869167202731, 2744.158931867943},
      {143, 146.51265277846505, 4237.8463486884475},
      {144, 28076.01137611955, 17421.611814708282},
      {145, 122.13011529516552, 2855.1891555402913},
      {146, 66.545608392300466, 1899.1451079723522},
      {147, 67.843015488148851, 4709.881251878247},
      {148, 179.59709535355535, 2380.8270725110547},
      {149, 75.301806125983475, 1823.7459751856782},
      {150, 74.652981344945317, 1455.7303911046238},
      {151, 100.14273838388837, 4286.1602627398788},
      {152, 25120.429422534515, 24451.972438071523},
      {153, 165.65192241080706, 2535.5696131885115},
      {154, 163.89877777227969, 2630.1052676769846},
      {155, 165.90927804443564, 3480.9221654574335},
      {156, 138.01981295462417, 1452.354398317091},
      {157, 155.98586768271562, 1972.2994032541965},
      {158, 168.82993220842198, 932.41214098656246},
      {159, 108.70387451135633, 2980.6740222384406},
      {160, 78059.361353852248, 25524.125059030612},
      {161, 290.33164431688851, 2795.6376593826471},
      {162, 82.725473798802511, 1345.3851371656722},
      {163, 235.20444851303876, 3060.6216459880652},
      {164, 54.541016378841107, 1650.2704245910788},
      {165, 131.95871146518877, 1285.0235263813163},
      {166, 152.7135088326983, 820.53518224359254},
      {167, 69.458572913058532, 2035.981754175074},
      {168, 5366.5689940125685, 19506.166874168204},
      {169, 86.43990301350884, 1972.0384235607264},
      {170, 146.99396308575388, 2561.8603443094494},
      {171, 59.729892622099065, 2771.086163225003},
      {172, 63.326409025681627, 1328.5062035804749},
      {173, 96.936988470483442, 1292.1862362083029},
      {174, 201.82901677470434, 1307.5331215386598},
      {175, 69.9891731406799, 2207.3535826213883},
      {176, 8439.3204958186943, 4926.8241961104195},
      {177, 57.45499529912415, 1652.9665564761945},
      {178, 94.9673016972636, 879.7069076546602},
      {179, 41.780884754317384, 2138.3052419181727},
      {180, 99.397451630461674, 1536.6737217189714},
      {181, 39.834929981691324, 1455.5517966771133},
      {182, 24.160581918947003, 2071.2529515305027},
      {183, 114.9652827947944, 2953.7725926243934},
      {184, 12696.54533128804, 114475.78736100974},
      {185, 69.021609184026914, 2107.3617825097667},
      {186, 25.025369884704833, 2117.2082599922724},
      {187, 33.02457320995596, 3322.3488172412312},
      {188, 83.779286456529263, 3455.0576997381186},
      {189, 58.103869563065963, 3780.4957712617525},
      {190, 23.295838487802463, 3230.4449834714292},
      {191, 23.998297788114208, 3384.2500321985144},
      {192, 28751.813286159631, 25693.245395612415},
      {193, 108.51668068682271, 2114.4923367535312},
      {194, 31.431916472858628, 1783.7861589318679},
      {195, 35.672710178633281, 3997.8335551453224},
      {196, 150.67289821366717, 45965.3282101919},
      {197, 39.514379731802663, 3721.672863091916},
      {198, 95.644796872680487, 2159.931867943159},
      {199, 43.206447622346481, 3790.0661572146137},
      {200, 27720.029180068286, 30623.58451036792},
      {201, 55.679390370626948, 5618.4326621731852},
      {202, 26.692275718739175, 5636.6078220924737},
      {203, 91.254332228215148, 6371.1617653372259},
      {204, 56.277999901034192, 5335.3434078907831},
      {205, 33.327913305952791, 5215.4466148628344},
      {206, 23.1998268098372, 3000.9659125059029},
      {207, 40.013479142956108, 3183.634782982012},
      {208, 11890.122653273294, 21048.844545571632},
      {209, 41.417383344054628, 2551.8852015627012},
      {210, 22.793606808847542, 2306.7041600480829},
      {211, 20.24546984017022, 3156.3955265530417},
      {212, 17.465792468702062, 2613.7808354441249},
      {213, 195.1869810480479, 3104.945262525222},
      {214, 21.820649215695976, 3056.3116816210877},
      {215, 26.68508090454748, 3223.9213068303784},
      {216, 16418.713335642537, 3944.5919804233031},
      {217, 39.425251125736061, 2196.1718112737731},
      {218, 56.336439210252856, 1736.7610440904994},
      {219, 14.083824038794596, 2592.4822049542781},
      {220, 37.664847345242222, 2334.4369553084616},
      {221, 118.27989014795388, 2937.3376550895118},
      {222, 33.866801919936663, 3730.7567509552227},
      {223, 59.533024889900538, 5919.6949727385909},
      {224, 11667.121351872927, 14320.959945047869},
      {225, 31.089291899648671, 6880.4117546043872},
      {226, 13.404389133554357, 6738.2337182844631},
      {227, 21.187411549309715, 7976.1910874511659},
      {228, 89.204804789945072, 6686.84033829906},
      {229, 16.820302835370381, 6274.9383505774267},
      {230, 10.550645751892722, 5748.9938178852017},
      {231, 14.096338265129397, 7194.4018803932513},
      {232, 2691.6707605522292, 65610.560340016309},
      {233, 60.017947449156317, 6384.4788992401154},
      {234, 31.910812014449007, 5208.0444768814668},
      {235, 52.319837696076007, 4792.0170008156956},
      {236, 102.47733188183483, 118588.8975657923},
      {237, 68.62079766440695, 3822.6592967844417},
      {238, 75.021935771191053, 4785.6392907740519},
      {239, 25.338369043495472, 6436.6231915167646},
      {240, 41280.646543619179, 61266.467651225692},
      {241, 1568.2530902073333, 6323.1032069720513},
      {242, 15.161121282596863, 5094.635727471773},
      {243, 48.038260181107425, 4268.8587558493964},
      {244, 352.26850908011284, 3413.8909114326193},
      {245, 24.200870899104359, 2852.939252135835},
      {246, 14.593621653718641, 2651.7705319194606},
      {247, 18.444648423969518, 3207.0947924269094},
      {248, 13186.79078628334, 3201.8194736616151},
      {249, 32.348874263941809, 1697.9772463830336},
      {250, 31.740704636548074, 757.19649680161422},
      {251, 52.65789499727844, 1234.7965483192374},
      {252, 111.80110346875155, 723.785600824282},
      {253, 97.249799594240187, 1286.1437771004164},
      {254, 172.72802711663121, 582334.49542781094},
      {255, 62.99471027759909, 2249.0812261194351},
      {256, 65434.324048691175, 1195419.8984244193},
      {257, 4768.9519916868721, 2348.0914008500408},
      {258, 230.61177198277994, 1516.6626883613103},
      {259, 150.92670592310355, 1506.6596402352639},
      {260, 384.0796674748874, 5785.2810715665655},
      {261, 114.77936562917512, 976.94260078135062},
      {262, 138.79850066801919, 380.47185849826127},
      {263, 152.91448364590033, 1076.0973253767227},
      {264, 6552.0402889801571, 27400.240844889024},
      {265, 95.457410064822611, 893.67668398231228},
      {266, 88.818922262358356, 448.18078392650153},
      {267, 100.5700826364491, 1025.1226119435023},
      {268, 739.088891088129, 453.807882196368},
      {269, 69.3592260873868, 655.02219550938048},
      {270, 35.978168142906625, 476.97827673549995},
      {271, 44.791404819634813, 1134.6853131842183},
      {272, 12067.757301202435, 4751.3826900785643},
      {273, 1762.5097827700529, 818.43279096724336},
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      {14235768, 5.9379484388143896e-05, 0.53088910831580316},
      {16777216, 0.0027710426047800477, 0.18593568883355513},
      {20971520, 0.00011381067841060914, 0.1459665994075473},
      {25165824, 0.0011480033648374488, 1.0194049714506503},
      {26214400, 2.9689742194071948e-05, 0.073069162409307511},
      {33554432, 8.906922658221585e-05, 0.34976173099214364},
      {41943040, 2.9689742194071948e-05, 0.028162967415103251},
      {47185920, 9.8965807313573165e-06, 0.021165156914094364},
      {50331648, 0.00011381067841060914, 0.58068947752543676},
      {100663296, 6.9276065119501214e-05, 0.18031168162108788},
      {201326592, 8.41209362165372e-05, 0.69093719143090193},
      {402653184, 1.9793161462714633e-05, 0.10003005194693684},
  };
  return e;
}

EmpiricalProfile Sierra() {
  static constexpr EmpiricalData::Entry e[] = {
      {1, 1576.0114639099133, 665.27870062753789},
      {2, 41.537714602178326, 3503.8033099544728},
      {3, 0.80655959633253338, 1108.7980189491818},
      {4, 6583.9188357639532, 17688.362926048972},
      {5, 20.567232785674729, 1100.7340962224682},
      {6, 1708.282653375177, 536.255014150363},
      {7, 129.45267983508708, 520.12723022025352},
      {8, 24887.908054888929, 52871.551310446659},
      {9, 726.11005476586058, 278.20788728928261},
      {10, 75.4141283613316, 294.3354251261228},
      {11, 143.16570057227247, 366.91202165620768},
      {12, 1998.0557319549566, 2913.1319675156883},
      {13, 103.240729801243, 306.43207825765967},
      {14, 56.056531905728875, 108.86378737541528},
      {15, 686.990055996554, 245.95151962593823},
      {16, 31904.569484954773, 73009.42408022641},
      {17, 1781.8361885422435, 10760.401132029039},
      {18, 1008.0283121038706, 20029.948997169926},
      {19, 2310.5420035690113, 15295.377014888643},
      {20, 3360.9065042151251, 24473.291374430908},
      {21, 1097.7542920435665, 6405.8330257167463},
      {22, 831.68440711340838, 7770.6642672572907},
      {23, 1708.8442495846409, 11292.630983142612},
      {24, 14439.138397637069, 166279.36723268119},
      {25, 865.762186942342, 4862.5911775562936},
      {26, 1442.2685065534429, 5401.8696936138795},
      {27, 742.4610854716633, 3917.0836717115785},
      {28, 3495.9981293458864, 4755.7377260981912},
      {29, 700.00827641375918, 5066.20401132029},
      {30, 1143.3206571903268, 5297.0340223944877},
      {31, 62321.578948987757, 96181.197489848651},
      {32, 127319.81705125839, 977266.63775070757},
      {33, 4821.6271367915824, 21435.305463270579},
      {34, 2692.851522983201, 6788.02356343054},
      {35, 2418.4032428773612, 8173.0412821459331},
      {36, 1683.0485139376037, 5780.6634674541647},
      {37, 2183.2974524644637, 11056.031315368524},
      {38, 1203.938557627223, 4517.9487510766585},
      {39, 1298.1689372961664, 7808.81838316722},
      {40, 32123.249233893297, 156894.31838316721},
      {41, 1111.1751030705802, 6380.7922357573516},
      {42, 931.5745923327795, 4362.0367909437673},
      {43, 1340.3888376099933, 4384.8965793035559},
      {44, 1303.9541258999445, 3211.55383290267},
      {45, 1127.7101593748077, 4751.8237972191464},
      {46, 888.75395360285518, 3567.059431524548},
      {47, 1140.0054519721864, 3504.5568475452196},
      {48, 33335.86899883084, 420682.08330257167},
      {49, 1237.5977847517076, 64200.88839670235},
      {50, 3022.4353270567967, 2594.0949920019689},
      {51, 761.4877484462495, 3517.4343546204013},
      {52, 492.79164974463112, 1978.2193306263073},
      {53, 365.74820626422991, 2703.9578565276238},
      {54, 892.41257768752689, 1439.4242647963579},
      {55, 3933.0832625684575, 1884.9592715639228},
      {56, 14933.220134145591, 153214.36138796603},
      {57, 599.35579964309886, 2620.8042328042329},
      {58, 463.50100301519905, 1246.3975021533161},
      {59, 474.74269891083628, 1755.9360772732866},
      {60, 983.56339302196784, 860.8322259136213},
      {61, 12003.206596517137, 1708.5614002707025},
      {62, 617.001772198634, 681.40771502399411},
      {63, 1101.3260476278383, 1751.3990402362494},
      {64, 40335.131628822841, 125407.50092284977},
      {65, 1222.974715402129, 2731.006029285099},
      {66, 357.82850286136238, 2978.5884090070135},
      {67, 801.96065472893974, 1849.5684754521965},
      {68, 252.647154021291, 548.78140765350065},
      {69, 712.38503476709127, 1620.9360157499693},
      {70, 236.87481385760876, 723.76479635781959},
      {71, 723.71980801181462, 1507.6026824166358},
      {72, 2161.7180850409204, 338596.87326196628},
      {73, 765.74098824687712, 1408.4344776670357},
      {74, 367.78380407359549, 396.76104343546206},
      {75, 508.99936003938217, 935.06373815676136},
      {76, 202.23003507476463, 605.21680817029653},
      {77, 561.18311488523784, 1147.542881752184},
      {78, 333.75035997784749, 618.11664820967144},
      {79, 462.21043628084425, 1160.8725852097946},
      {80, 13645.153978216726, 109177.32225913621},
      {81, 713.230964248354, 1240.1339977851605},
      {82, 104.42480462740754, 605.12280054140524},
      {83, 357.16821118700386, 726.739694844346},
      {84, 97.434582487231552, 375.63338255198721},
      {85, 386.40829487416158, 649.12212378491449},
      {86, 161.08879453572087, 319.86077273286577},
      {87, 310.21518675773797, 449.54737295434973},
      {88, 6685.139942157406, 32672.589331856772},
      {89, 378.51078702849054, 616.52977728559119},
      {90, 94.609617869669563, 351.44149132521227},
      {91, 313.98183496400219, 3578.3592346499322},
      {92, 157.52813365331363, 433.75882859603792},
      {93, 439.68041351301457, 501.62507690414668},
      {94, 170.46695587963816, 352.78479143595422},
      {95, 387.01524213894527, 408.5564168819983},
      {96, 7376.9568149652332, 592056.92611049593},
      {97, 278.67042643529629, 493.33247200689061},
      {98, 54.421617131253463, 527.6097575981297},
      {99, 285.21004861239311, 1135.0131044665929},
      {100, 124.28266568211187, 558.72388335179028},
      {101, 311.91586363916065, 657.49267872523683},
      {102, 174.29520644883391, 453.593946105574},
      {103, 398.83434865546735, 575.12310815799185},
      {104, 7843.0419543412709, 270310.93152454781},
      {105, 252.13840379053596, 1009.1276608834748},
      {106, 79.859657867208171, 1330.8167220376522},
      {107, 466.01361762353088, 1607.2910668143227},
      {108, 148.39929850470739, 2157.3641565153193},
      {109, 1283.2440034459419, 2575.8184446905375},
      {110, 224.10574118515783, 2250.96880767811},
      {111, 396.52644760322443, 4551.0126122800539},
      {112, 22047.550132299551, 55384.474775439892},
      {113, 635.13687157713366, 2218.8844592100404},
      {114, 191.81222693988062, 2670.989233419466},
      {115, 297.28576087625379, 2499.3774455518642},
      {116, 123.09525567657374, 2395.5513719699766},
      {117, 208.4268598855455, 2454.5182724252491},
      {118, 74.517469694172661, 1881.2032115171651},
      {119, 355.96714048366255, 2391.5159960625078},
      {120, 6208.1713986831583, 11813.635658914729},
      {121, 1334.428896683281, 1705.3064476436568},
      {122, 84.449806165774419, 1743.1074197120709},
      {123, 243.15607039566797, 1534.1909068536975},
      {124, 108.97760137837672, 1054.8813830441738},
      {125, 238.19254815088303, 1160.9718838439769},
      {126, 93.4232416466679, 996.66678971330134},
      {127, 189.11415297520153, 1081.0861326442721},
      {128, 15074.233954833549, 148166.62882982651},
      {129, 261.99411728509017, 736.30220253476068},
      {130, 56.358402559842474, 465.03340716131413},
      {131, 189.48180419666483, 692.62341577457858},
      {132, 465.1501938342256, 583.30940076288914},
      {133, 163.82609685557813, 786.48406546080969},
      {134, 45.309937849978461, 425.8345637996801},
      {135, 287.10926712202325, 428.7515688445921},
      {136, 15500.622693988062, 13531.785898855665},
      {137, 113.74639714479109, 361.99181739879413},
      {138, 198.40339056058087, 284.26258151839545},
      {139, 183.0394437265399, 211.68549280177186},
      {140, 85.348630853485943, 169.3482834994463},
      {141, 170.68147190942096, 216.38931955211024},
      {142, 107.93964679096671, 213.92475698289653},
      {143, 87.5953602855209, 229.60588162913746},
      {144, 1453.6779028982833, 12050.522640580781},
      {145, 183.88688080733493, 213.10262089331857},
      {146, 38.1175189219125, 193.74775439891718},
      {147, 88.051412220786418, 200.40125507567367},
      {148, 46.145467971201775, 273.18333948566504},
      {149, 141.35411974647715, 275.400947459087},
      {150, 62.878813611470065, 290.32065952996186},
      {151, 93.1147744754169, 293.3439768672327},
      {152, 5747.630471970956, 47035.62310815799},
      {153, 126.61036859270199, 304.433062630737},
      {154, 44.915149836933111, 6748.3922111480251},
      {155, 75.588179188972987, 408.66598991017594},
      {156, 72.648753922835525, 450.40002460932692},
      {157, 66.495218755768875, 491.32896517780239},
      {158, 134.84191126699895, 420.3596653131537},
      {159, 63.125204602793673, 532.85646610065214},
      {160, 6070.8064549873852, 96257.847483696314},
      {161, 444.6374623100117, 530.77297895902552},
      {162, 28.10801796812504, 407.61111111111109},
      {163, 46.607119561873112, 396.61437184693},
      {164, 50.275109224047753, 501.81530700135352},
      {165, 53.794197280167374, 399.18020179648084},
      {166, 26.934619408036429, 244.3095238095238},
      {167, 48.7907451849117, 302.04214347237604},
      {168, 1583.0048858531782, 8162.1488249046388},
      {169, 88.335917789674482, 284.08078011566386},
      {170, 22.442545074149283, 3586.8551125876706},
      {171, 139.06306073472402, 174.114187276978},
      {172, 31.830182757984122, 171.3651408883967},
      {173, 66.900812257707216, 253.47532914974775},
      {174, 45.085034767091258, 245.40919158361018},
      {175, 49.118737308473328, 352.44462901439647},
      {176, 1674.8411913113039, 8039.8848898732622},
      {177, 56.021690972863212, 189.35775809031622},
      {178, 22.086117777367548, 185.15805340223946},
      {179, 33.935973170881795, 175.24369385997292},
      {180, 38.036902344471109, 173.73126614987081},
      {181, 62.743997292474312, 194.56650670604159},
      {182, 30.843818841917422, 194.90267011197244},
      {183, 69.179724324656945, 278.91245231942906},
      {184, 8873.65843332718, 13209.722283745539},
      {185, 82.541000553812069, 203.80829334317707},
      {186, 31.296141775890714, 181.45816414421066},
      {187, 91.664931388837616, 164.49101759566875},
      {188, 38.892369700326135, 169.36347975882859},
      {189, 56.154624330810414, 173.73200442967885},
      {190, 56.8929050519968, 170.2041958902424},
      {191, 43.128693618854221, 159.45047372954349},
      {192, 2310.7571780198141, 62678.04891103728},
      {193, 107.34336348532398, 210.93460071367048},
      {194, 39.548876992185093, 203.80041835855789},
      {195, 33.3595040305212, 170.4537959886797},
      {196, 40.7103070580272, 155.40814568721547},
      {197, 65.96736200849179, 174.02005660145196},
      {198, 15.221149467725063, 165.79764980927771},
      {199, 41.115845178758228, 189.213608957795},
      {200, 4389.0310688573009, 4752.5083671711582},
      {201, 48.065275983016427, 257.458594807432},
      {202, 25.739437573072426, 185.65214716377508},
      {203, 76.314232970278752, 166.11086501784177},
      {204, 30.455516583594857, 133.07481235388212},
      {205, 55.619592640452893, 144.86243386243387},
      {206, 45.365552889052978, 137.88218284729913},
      {207, 36.18050581502677, 171.07315122431402},
      {208, 1439.4381514983693, 2857.1557770394979},
      {209, 45.036317765060609, 187.66389811738648},
      {210, 23.843505015075994, 133.94081456872155},
      {211, 24.637677681373454, 240.66309831426111},
      {212, 14.768795766414375, 131.34926787252368},
      {213, 36.4224540028306, 268.46216315983759},
      {214, 20.573429327426005, 137.54362003199213},
      {215, 28.714491415912867, 346.09234649932324},
      {216, 313.70012306934956, 2574.769964316476},
      {217, 38.293778844378807, 428.76418112464626},
      {218, 10.086253153652082, 119.10908084163898},
      {219, 21.035560888560703, 382.38735080595546},
      {220, 10.431850347670913, 134.94936630983142},
      {221, 21.90017845055689, 264.28620647225296},
      {222, 34.779324349270816, 122.85228251507321},
      {223, 57.122847824749243, 273.79260489725607},
      {224, 1756.8822718601932, 74060.45059677618},
      {225, 25.026115315980554, 315.49895410360529},
      {226, 17.534982462617684, 113.72474467823305},
      {227, 33.107464156051932, 419.94776670358067},
      {228, 22.174696941726662, 123.80749354005168},
      {229, 32.032416466678974, 403.94868955334073},
      {230, 9.5345578733616385, 120.58108773225052},
      {231, 24.473730847332472, 320.7390180878553},
      {232, 361.44967078948986, 14013.44062999877},
      {233, 36.656950341517444, 364.55770887166238},
      {234, 17.279084364039136, 132.67774086378736},
      {235, 18.813537628453634, 303.39387227759323},
      {236, 5.8235185527044493, 132.00467577211762},
      {237, 27.04204048981601, 307.43060169804357},
      {238, 13.663165343671158, 125.68641565153193},
      {239, 48.124558488708388, 228.79045158114926},
      {240, 651.29328656698044, 2585.0816414421065},
      {241, 116.37953972063258, 300.52220991755877},
      {242, 15.429770475663036, 138.22591362126246},
      {243, 21.619032674912312, 321.81567614125754},
      {244, 5.5342932742600457, 190.38913498215823},
      {245, 18.291145160297827, 261.45539559493045},
      {246, 7.2991508214879088, 143.64396456256921},
      {247, 17.395957171866346, 238.27107173618802},
      {248, 284.685262445388, 340.9780361757106},
      {249, 31.336379299735402, 214.07856527623969},
      {250, 12.896424835394745, 146.91823551125876},
      {251, 67.189502184480958, 207.40008613264428},
      {252, 106.3180727339856, 146.66722037652269},
      {253, 30.026841425143068, 176.78165374677002},
      {254, 23.59794474186204, 138.09942168081702},
      {255, 29.937634607101103, 165.3154300479882},
      {256, 5512.1762537689992, 62354.933124154057},
      {257, 82.235308596394063, 283.01156638365939},
      {258, 25.489852932127253, 125.01993355481727},
      {259, 78.136157774906167, 153.60440506952136},
      {260, 44.148840071380221, 149.57216685123663},
      {261, 76.25712879207434, 169.37959886797097},
      {262, 176.60782721063319, 136.52368647717486},
      {263, 55.902387545381821, 145.89442598744924},
      {264, 1284.4287613069964, 7881.8714777900823},
      {265, 125.74301273767769, 167.12649194044542},
      {266, 131.24498184727094, 128.22259136212625},
      {267, 130.30517506614979, 135.6959517657192},
      {268, 188.13111808504092, 141.26738033714778},
      {269, 103.90916251307611, 198.08588655100283},
      {270, 320.08629007445694, 129.28977482465854},
      {271, 294.624810780875, 148.50190722283745},
      {272, 363.91239923697003, 11396.124953857512},
      {273, 121.00659036366993, 148.1520241171404},
      {274, 111.51559904005907, 141.76682662729175},
      {275, 118.07073410867024, 138.7441245231943},
      {276, 220.31598055504276, 128.32859603789836},
      {277, 115.4711833117962, 134.71176325827489},
      {278, 130.51901421450987, 134.37590746893073},
      {279, 112.72305088917605, 133.36889381075429},
      {280, 678.28444403421327, 895.28848283499451},
      {281, 143.8207556458064, 146.02319429063616},
      {282, 208.29637560765491, 142.1046511627907},
      {283, 116.86843271183312, 147.36717115786882},
      {284, 66.56872192480462, 127.99212501538084},
      {285, 51.263251492215865, 148.26184323858743},
      {286, 105.65832256476524, 127.99181739879414},
      {287, 72.508824072364774, 130.791497477544},
      {288, 308.09939080671961, 2688.923711086502},
      {289, 161.74627407544151, 139.76738033714778},
      {290, 130.7653129038213, 128.51894918173988},
      {291, 32.257990277521387, 137.43330872400639},
      {292, 24.752402929050518, 146.02983880890858},
      {293, 25.558322564765245, 132.44610557401256},
      {294, 43.67971201772199, 132.76307370493416},
      {295, 39.304461263922221, 140.82859603789836},
      {296, 4438.2435542428157, 31677.047742094255},
      {297, 59.026521444834167, 138.60169804355851},
      {298, 52.832342625069224, 127.35222099175587},
      {299, 17.360254753553626, 136.37209302325581},
      {300, 23.718964986770043, 127.24535498954104},
      {301, 22.828613623777, 135.73606496862311},
      {302, 216.2296350993785, 119.92266519010705},
      {303, 23.730804258199495, 134.24984619170667},
      {304, 567.48449326195316, 1669.237849144826},
      {305, 17.51715586733124, 120.23132767318813},
      {306, 28.64119131130392, 121.34311554078995},
      {307, 10.024220047997046, 122.85529715762274},
      {308, 59.620017229708942, 119.02337886058817},
      {309, 15.994609562488462, 140.4905869324474},
      {310, 30.0234447110947, 117.91571305524793},
      {311, 15.551406067318934, 132.9318321643903},
      {312, 310.10761183927144, 3538.1060046757721},
      {313, 15.268321949418498, 143.31290759197736},
      {314, 28.308953295181833, 127.69269102990033},
      {315, 30.906621131007324, 132.124953857512},
      {316, 86.20165528275183, 119.93152454780362},
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      {9694, 19.471121777121407, 1.6766949673926419},
      {9704, 4.779324349270814, 37.117755629383531},
      {10072, 59.586548520091107, 95.985172880521745},
      {10240, 16.492105101224542, 15.016242155777038},
      {12288, 43.993735770106468, 114.7839301095115},
      {16384, 162.1003569011138, 37916.196320905619},
      {16416, 17.076204541259, 6.1049587793773847},
      {19201, 35.035019383422558, 49.035868094007611},
      {19203, 1.4168112731524214, 0.023624953857511996},
      {19205, 0.70396283305642726, 0.032484311554078993},
      {19206, 0.7413820687957664, 0.023686477174849268},
      {19207, 0.728810534736324, 0.0073827980804724988},
      {19208, 0.7741431296535598, 0.011812476928755998},
      {19209, 1.0272352470617192, 0.014765596160944998},
      {19210, 0.98003199803089036, 0.014765596160944998},
      {19212, 0.97099870777182939, 0.016242155777039496},
      {19213, 0.80363054581256543, 0.014827119478282269},
      {19214, 2.1623284720940248, 0.017718715393133997},
      {19215, 1.5261337763829919, 0.0088593576965669985},
      {19216, 1.247677066026706, 0.0014765596160944998},
      {19217, 0.99606793428096729, 0.0044296788482834993},
      {19219, 1.1118023506245769, 0.034022394487510765},
      {19220, 0.99550181527290627, 0.028116156023132766},
      {19221, 0.94106208848686235, 0.011812476928755998},
      {19222, 1.0884130207371854, 0.0088593576965669985},
      {19223, 1.1265768260414744, 0.014765596160944998},
      {19224, 1.5901667589686788, 0.037037037037037035},
      {19226, 1.1993784997846286, 0.025101513473606497},
      {19227, 1.0582917974278505, 0.005906238464377999},
      {19228, 1.2188911451602977, 0.011812476928755998},
      {19229, 1.2483047197095563, 0.016242155777039496},
      {19230, 1.1959694788013044, 0.0088593576965669985},
      {19231, 1.2906528828995139, 0.016242155777039496},
      {19233, 1.1278136730047381, 0.029531192321889995},
      {19234, 2.1259122515537507, 0.0088593576965669985},
      {19235, 1.4920435665497507, 0.011812476928755998},
      {19236, 1.0789797550919944, 0.011812476928755998},
      {19237, 1.1023137037720756, 0.014765596160944998},
      {19238, 1.033677927512153, 0.005906238464377999},
      {19240, 1.117894283428712, 0.036975513719699767},
      {19241, 1.1446864808319488, 0.005906238464377999},
      {19242, 1.1157221094086518, 0.0103359173126615},
      {19243, 1.0554796627899821, 0.013289036544850499},
      {19244, 1.1555719648021661, 0.0088593576965669985},
      {19245, 1.0810596270998707, 0.0073827980804724988},
      {19247, 1.0303919758784075, 0.026639596407038266},
      {19248, 1.2685496277152175, 0.0103359173126615},
      {19249, 1.2623838533013354, 0.017780238710471269},
      {19250, 0.992271244846471, 0.005906238464377999},
      {19251, 1.0186450064611408, 0.0073827980804724988},
      {19252, 1.0061165466740509, 0.005906238464377999},
      {19254, 1.0801119931081165, 0.031069275255321768},
      {19255, 0.996172543228109, 0.0088593576965669985},
      {19256, 1.5392406621131007, 0.0073827980804724988},
      {19257, 1.4907082641068241, 0.016242155777039496},
      {19258, 1.4250199987693064, 0.0103359173126615},
      {19259, 1.3769121900190757, 0.0103359173126615},
      {19261, 1.1277521383299489, 0.037037037037037035},
      {19262, 1.0071195618731155, 0.016242155777039496},
      {19263, 1.0862839209894777, 0.014765596160944998},
      {19264, 0.96890037536151619, 0.0044296788482834993},
      {19265, 1.1495723340102149, 0.0103359173126615},
      {19266, 1.1185096301766044, 0.0044296788482834993},
      {19268, 1.0466063626853732, 0.017718715393133997},
      {19269, 1.0158759460956248, 0.025101513473606497},
      {19270, 0.92314934465571352, 0.013289036544850499},
      {19271, 0.94346809427112177, 0.0044296788482834993},
      {19272, 0.92738293028121344, 0.0103359173126615},
      {19273, 0.99688634545566424, 0.034083917804848041},
      {19275, 0.99539720632576456, 0.023624953857511996},
      {19276, 0.91094701864500649, 0.0073827980804724988},
      {19277, 0.96550981478062892, 0.026639596407038269},
      {19278, 0.93659467109716321, 0.0073827980804724988},
      {19279, 0.90060919328041356, 0.0103359173126615},
      {19280, 0.9285459356347302, 0.005906238464377999},
      {19282, 0.89416651282997961, 0.026578073089700997},
      {19283, 1.0291428219801859, 0.023624953857511996},
      {19284, 1.0739585256291921, 0.0088593576965669985},
      {19285, 0.91580825795335674, 0.0088593576965669985},
      {19286, 0.9362193095809489, 0.034083917804848041},
      {19287, 1.1508337948433942, 0.017718715393133997},
      {19289, 1.0459910159374808, 0.023624953857511996},
      {19290, 0.93857608762537692, 0.0088593576965669985},
      {19291, 0.87408159497877058, 0.020733357942660267},
      {19292, 0.8628022890899022, 0.011812476928755998},
      {19293, 0.840600578425943, 0.0221483942414175},
      {19294, 0.776081471909421, 0.013350559862187769},
      {19296, 0.92610916251307607, 0.01925679832656577},
      {19297, 0.90828256722663225, 0.0103359173126615},
      {19298, 0.83509322503230565, 0.011812476928755998},
      {19299, 0.83802842901975261, 0.011812476928755998},
      {19300, 0.81768506553442866, 0.011812476928755998},
      {19301, 0.8937788443788075, 0.026639596407038269},
      {19303, 0.85884560950095379, 0.038452073335794271},
      {19304, 0.81365454433573314, 0.017718715393133997},
      {19305, 0.82092794289582183, 0.013289036544850499},
      {19306, 0.74517875823026281, 0.0088593576965669985},
      {19307, 0.84258199495415664, 0.013289036544850499},
      {19308, 0.87017414312965358, 0.011812476928755998},
      {19310, 0.7818595778721309, 0.025101513473606497},
      {19311, 0.74256968801919887, 0.026639596407038269},
      {19312, 0.73110577810596267, 0.01925679832656577},
      {19313, 0.75514737554612021, 0.017780238710471269},
      {19314, 0.85854408959448647, 0.011812476928755998},
      {19315, 0.72381391914343729, 0.00892088101390427},
      {19317, 0.77394621869423419, 0.019195275009228498},
      {19318, 0.71554981231924186, 0.014765596160944998},
      {19319, 0.7355485816257461, 0.011812476928755998},
      {19320, 0.93512399236970034, 0.013289036544850499},
      {19321, 0.886333148729309, 0.0103359173126615},
      {19322, 0.7028121346378684, 0.014765596160944998},
      {19324, 0.76468525013845312, 0.023624953857511996},
      {19325, 0.71274998461633132, 0.005906238464377999},
      {19326, 0.69832010337825368, 0.005906238464377999},
      {19328, 1.3623161651590672, 0.028054632705795494},
      {19329, 0.69929850470740262, 0.019195275009228498},
      {19331, 0.80934096363300712, 0.026578073089700997},
      {19332, 0.73382561073164732, 0.01925679832656577},
      {19333, 0.81527290628269034, 0.005906238464377999},
      {19334, 0.70567965048304715, 0.019195275009228498},
      {19335, 0.76896191003630543, 0.025163036790943769},
      {19336, 0.67695526429142827, 0.017780238710471269},
      {19340, 2.0128299796935574, 0.035498954103605262},
      {19345, 2.70251676819888, 0.097575981296911529},
      {19346, 0.68351486062396161, 0.0088593576965669985},
      {19347, 0.74592948126269154, 0.0073827980804724988},
      {19349, 1.3173958525629192, 0.020671834625322995},
      {19352, 1.392351239923697, 0.038452073335794271},
      {19353, 0.69267737370008, 0.019195275009228498},
      {19355, 1.3722909359424036, 0.023624953857511996},
      {19356, 0.69543412713063812, 0.013289036544850499},
      {19369, 6.6243861916189779, 0.19662852220991753},
      {19370, 0.70020306442680447, 0.032607358188753537},
      {19383, 6.8182388776075324, 0.20727205610926536},
      {19384, 1.2781059627099871, 0.011812476928755998},
      {19391, 3.2474924620023389, 0.093023255813953473},
      {20480, 96.098418558857944, 20.020794881259992},
      {24576, 37.052962894591118, 63.728743693859975},
      {28000, 23.620915635960866, 66.367540297772862},
      {30000, 13.872395544889544, 25.136397194536723},
      {30488, 5.6599040059073307, 5.8712932201304309},
      {32756, 30.30220294135745, 32.39916328288421},
      {32768, 482.7799150821487, 133.161252614741},
      {36872, 8.7377022952433716, 51.03919035314383},
      {40960, 7.7954587410005507, 45.701365817644877},
      {48592, 14.296683281028866, 82.324473975636764},
      {49152, 1.2814903698233955, 6.028546819244494},
      {53040, 6.9704448956987273, 59.9043927648579},
      {65536, 1731.49836317765, 2872.3071859234665},
      {65544, 0.56321457141099007, 0.94696690045527254},
      {76490, 33.615888253030576, 3.8538205980066431},
      {81920, 470.86407605685815, 1.6826012058570208},
      {98312, 32.861454679712025, 8.7478774455518646},
      {104864, 5.2648513937603845, 0.5563553586809401},
      {106496, 1.2319303427481385, 0.09314630244862801},
      {128000, 9.3091194388037675, 4.4190353143841516},
      {131072, 1.0104301273767768, 44.435277470161132},
      {196744, 13.879632022644756, 9.31905992371108},
      {262144, 6.2496830964248371, 48.910852713178272},
      {274432, 0.20116915882099573, 1.1110495877937729},
      {393256, 0.675244600332287, 1.8602805463270584},
      {524288, 0.6249769244969533, 15.266949673926417},
      {1048576, 0.09222817057411857, 10.168881506090793},
      {2097152, 0.030675035382437984, 1.2770394979697297},
      {2097168, 0.012934588640699034, 0.0022148394241417496},
      {2800120, 0.025167681988800684, 0.025163036790943775},
      {3145728, 0.35501199926158394, 1.1722037652270212},
      {3670024, 0.0011260845486431607, 0.13676633444075306},
      {4194304, 0.0083256414989846816, 0.16383659406915244},
      {4194320, 0.2953848993908067, 0.00670604158976252},
      {5600064, 0.0041412836133161044, 0.0036298757228989792},
      {8388608, 0.0011568518860377822, 0.049464747139165745},
      {16777216, 0.00011076241462063873, 2.5840408514827122},
      {33554432, 5.5381207310319367e-05, 0.010582010582010581},
  };
  return e;
}

EmpiricalProfile Sigma() {
  static constexpr EmpiricalData::Entry e[] = {
      {1, 114.9947654491508, 227.07222782557105},
      {2, 8.63298291385308, 18.663470780183921},
      {3, 4.6936630345815429, 41.992809255413825},
      {4, 65.711226212400248, 654.77687333135566},
      {5, 5.1127391549007575, 241.07002076535153},
      {6, 3.5202412011458972, 36.549296944526844},
      {7, 8.4653609064865964, 254.28981311183625},
      {8, 139.13336530591366, 7098.3404924354791},
      {9, 30.383378094945776, 118.590803915752},
      {10, 14.919298649478208, 41.992809255413825},
      {11, 40.273646920401063, 33.04989617324236},
      {12, 33.442602823818291, 43.159276179175322},
      {13, 13.284888479639861, 48.991610797982794},
      {14, 8.5073421833435638, 16.719359240581429},
      {15, 5.448068856148967, 75.431527736576683},
      {16, 391.59036346429303, 10177.437876001186},
      {17, 46.83322974217311, 1280.5880154256897},
      {18, 22.107165694700225, 1422.8965766834767},
      {19, 311.86434417843259, 2209.8878077721743},
      {20, 31.934641651319829, 1805.1106615247702},
      {21, 114.74561080417433, 1122.1427588252743},
      {22, 57.205390577041129, 7640.1686502521507},
      {23, 60.160428176795577, 1146.8325838030257},
      {24, 334.0783468897074, 11026.269273212696},
      {25, 19.089656230816452, 880.10065855829134},
      {26, 16.554188408021282, 1014.6342568970632},
      {27, 22.693857427869858, 1747.0048531593},
      {28, 23.196829598935953, 3870.8161139127856},
      {29, 33.548136638019237, 1398.6103945416789},
      {30, 28.163061438510333, 6912.4770453871251},
      {31, 412.59280872723554, 7645.2454701868883},
      {32, 2904.4549787702067, 126759.92843666568},
      {33, 93.487198178841822, 59930.6054820528},
      {34, 20.005752506650296, 1092.1069593592406},
      {35, 17.672577757315327, 1073.3141382379115},
      {36, 44.048195467567012, 955.75555028181543},
      {37, 30.804877736852873, 1372.7163097003856},
      {38, 27.773386024145694, 4595.292874517947},
      {39, 58.786222375690606, 5980.729409670721},
      {40, 590.40170222017593, 31671.336422426579},
      {41, 64.764422191528539, 1179.0770335212103},
      {42, 65.519571055862485, 616.43298724414126},
      {43, 23.037418150194394, 883.302806288935},
      {44, 13.775033251483528, 955.23696232571933},
      {45, 54.162176437487211, 744.61829724117467},
      {46, 21.612459075097195, 345.67406704242063},
      {47, 16.024276140781666, 790.629759715218},
      {48, 1089.248387303049, 65617.900955206176},
      {49, 26.791994065889092, 1576.0236725007417},
      {50, 31.884241354614282, 289.09219816078314},
      {51, 21.343657918968692, 773.56384455651141},
      {52, 28.929652649887455, 249.72397508157817},
      {53, 23.858288571720891, 684.71839810145354},
      {54, 19.992004297114793, 146.87913378819343},
      {55, 19.153720329445466, 612.39638089587663},
      {56, 71.637352926130546, 13593.205731237022},
      {57, 28.75128657663188, 721.07263126668647},
      {58, 19.310880908532841, 187.21979234648472},
      {59, 19.5309046961326, 383.96374962919015},
      {60, 20.641495293636179, 140.75625037080985},
      {61, 48.082820493145078, 547.76160189854647},
      {62, 17.299163597298957, 185.27819638089588},
      {63, 79.493348424391243, 413.61363393651737},
      {64, 266.89913418252507, 11799.166905962622},
      {65, 18.9793930325353, 380.75804212399879},
      {66, 16.531523685287496, 148.30587956096113},
      {67, 25.970037855535093, 343.97320676357162},
      {68, 16.036864385103335, 158.02705428656185},
      {69, 17.579345713116432, 269.47030554731532},
      {70, 16.80812487210968, 88.268051023435177},
      {71, 15.35779619398404, 260.13801245921093},
      {72, 947.87238464293023, 6176.7425808365469},
      {73, 17.956507059545732, 339.54036191041234},
      {74, 13.44654312461633, 76.913746662711361},
      {75, 17.176832668303664, 274.4475348561258},
      {76, 12.583085226110088, 113.15420943340256},
      {77, 14.838125383670963, 375.23644022545238},
      {78, 13.806925260896255, 156.16061702758824},
      {79, 16.145885768365051, 281.83575200237317},
      {80, 806.39591134642933, 64544.7161673094},
      {81, 12.329175618989154, 292.91371106496587},
      {82, 11.847185134029056, 144.32645505784635},
      {83, 12.510792664211172, 179.64219519430435},
      {84, 11.141653877634541, 135.57565114209433},
      {85, 12.573660988336403, 225.64261050133493},
      {86, 12.671457438101084, 85.415223969148627},
      {87, 12.385058573767138, 144.63973894986651},
      {88, 15.472587988541028, 3339.7532720261052},
      {89, 10.093858706773071, 137.63964402254524},
      {90, 9.89128043789646, 65.583553841590032},
      {91, 11.316298342541437, 94.483025808365468},
      {92, 10.205623337425823, 77.573111836250376},
      {93, 9.2835545835891136, 159.21954316226638},
      {94, 7.97030642520974, 86.45178285375259},
      {95, 9.9471646715776547, 135.37497478493029},
      {96, 69.091951862083079, 5165.1150875111243},
      {97, 8.610449918150195, 110.53959062592702},
      {98, 12.490566809903827, 67.6589380005933},
      {99, 14.831757724575404, 92.3189913972115},
      {100, 10.508508543073461, 59.270210619994067},
      {101, 9.99354409658277, 87.152026105013348},
      {102, 8.3469024964190712, 40.994161969741917},
      {103, 7.2631611929609168, 60.045221002669834},
      {104, 32.094697667280542, 4279.179115989321},
      {105, 4.4070237364436258, 50.768519727083948},
      {106, 4.6525219971352572, 51.323808958765945},
      {107, 4.5088244321669739, 29.550293681400177},
      {108, 5.670433036627788, 15.108454464550578},
      {109, 4.2094229588704728, 27.10615247700979},
      {110, 3.9639323715981174, 19.885066745772768},
      {111, 4.1914735522815629, 28.439181251854048},
      {112, 64.636811950071618, 4566.5582675763872},
      {113, 4.0921475342746065, 36.306876297834471},
      {114, 3.7882238592183342, 14.04643132601602},
      {115, 4.1078460712093312, 20.316487689113021},
      {116, 5.601067884182525, 23.329587659448237},
      {117, 3.9872851442602824, 31.009077425096411},
      {118, 8.4038942602823816, 15.601791753188964},
      {119, 9.7816835481890738, 22.989676653811927},
      {120, 52.13609064865971, 20973.876060516166},
      {121, 18.893056834458768, 53.320284781963807},
      {122, 6.8635205647636583, 7.8252032037970931},
      {123, 4.3383236136689174, 13.609018095520616},
      {124, 4.5636164825046039, 14.678184514980718},
      {125, 3.5419569776959281, 26.683310590329278},
      {126, 2.7507993145078782, 6.3670958172649064},
      {127, 2.4678573255576017, 10.0609196084248},
      {128, 214.899512737876, 1920.9262770691189},
      {129, 3.6095879373848989, 24.323737763274991},
      {130, 1.923634131368938, 11.103411450608128},
      {131, 2.2123964088397789, 11.924259863541975},
      {132, 77.200510282381828, 52.190186888163751},
      {133, 5.0299519132392057, 7.949510530999703},
      {134, 1.797877020667076, 4.7524176802135862},
      {135, 1.9143083691426233, 10.023292791456541},
      {136, 31.478859729895643, 3201.5336458024326},
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      {5192, 0.25922856558215673, 0.21890240284781964},
      {5196, 0.18273480662983424, 0.18966478789676655},
      {5823, 7.96759131368938, 38.032916048650243},
      {6000, 2.3811233885819516, 9.87005636309701},
      {6001, 0.28192526089625536, 0.059519430436072385},
      {6144, 1.6155859934520163, 110.88380895876594},
      {6152, 0.088478360957642721, 17.543174132304951},
      {7184, 10.149704573357884, 56.761518837140308},
      {7696, 5.72886868221813, 48.8308632453278},
      {8000, 2.1544608144055659, 30.364995550281819},
      {8176, 2.0504821465111522, 42.007048353604269},
      {8192, 540.469381778187, 3957.9346900029664},
      {8200, 0.1183560978105177, 2.8909641056066451},
      {9072, 5.0807115817474937, 18.044817561554428},
      {9704, 2.5587310722324532, 16.734262830020779},
      {10072, 1.1685926949048497, 28.51458914268764},
      {12288, 6.6037113771229778, 33.097834470483548},
      {12296, 0.017903366073255579, 3.8934322159596557},
      {12344, 0.10097196644157971, 6.1816196974191637},
      {16384, 6.6186131573562541, 12.93294571343815},
      {16392, 0.021236187845303865, 1.9422960545832095},
      {16440, 0.058605739717618163, 0.9672619400771284},
      {17816, 0.96706440556578654, 2.1276416493622059},
      {18440, 0.31248081645181097, 3.4683358053989903},
      {20480, 0.85003453038674, 1.42889350341145},
      {22001, 0.515290566809904, 0.40654998516760582},
      {22205, 0.040373695518723149, 0.87986947493325474},
      {22536, 0.065689584612236562, 0.87862355384159008},
      {22584, 0.00846889707386945, 1.766716107979827},
      {24584, 0.32686464088397782, 3.6921269652921986},
      {24632, 0.0076874872109678749, 0.81347967962029066},
      {32756, 1.0411333640270106, 1.792061702758825},
      {32768, 27.079940403110292, 13.417276772471077},
      {32784, 0.030776805811336197, 0.92098487095817261},
      {36872, 0.1261458972784939, 7.1491070898843034},
      {40960, 0.071197820748925708, 1.0139305843963211},
      {45064, 0.05816068139963166, 0.94030258083654716},
      {45552, 0.0047460098219766732, 0.90297241174725607},
      {49208, 0.034602005320237363, 1.8761673094037377},
      {53412, 0.029840648659709434, 0.91977454761198474},
      {65536, 176.51800312052387, 2.4566953426282989},
      {65537, 0.000698281154082259, 0.84814001779887271},
      {65544, 0.036942398199304276, 0.013444081874814596},
      {65552, 2.6477836607325558, 0.37236428359537227},
      {74256, 0.43742198690403095, 0.96741619697419146},
      {76490, 1.5655233271945981, 0.01249480866211806},
      {76590, 3.9853322590546352, 0.014512014239098191},
      {76606, 27.064743196234907, 0.0033105903292791456},
      {81920, 0.38439482299979549, 0.84739246514387556},
      {93450, 0.19440607734806631, 0.053705132008306164},
      {93453, 0.00491866175567833, 5.9329575793533079e-05},
      {93472, 0.0059852670349907922, 5.9329575793533079e-05},
      {93486, 0.0075122774708410072, 5.9329575793533079e-05},
      {93487, 0.0068984039287906694, 5.9329575793533079e-05},
      {93519, 0.010710814405565787, 5.9329575793533079e-05},
      {93537, 0.012373388581952117, 5.9329575793533079e-05},
      {93550, 0.013226417024759567, 5.9329575793533079e-05},
      {93555, 0.015777828933906283, 5.9329575793533079e-05},
      {93557, 0.01526498874565173, 5.9329575793533079e-05},
      {93566, 0.01777036013914467, 0.00011865915158706616},
      {93575, 0.01755550439942705, 5.9329575793533079e-05},
      {93589, 0.019094024964190711, 5.9329575793533079e-05},
      {93600, 0.019432934315531, 5.9329575793533079e-05},
      {93601, 0.018925209740126868, 5.9329575793533079e-05},
      {93603, 0.019027521997135258, 5.9329575793533079e-05},
      {93606, 0.020545580110497237, 5.9329575793533079e-05},
      {93617, 0.022521485573971763, 5.9329575793533079e-05},
      {93624, 0.022559852670349909, 5.9329575793533079e-05},
      {93627, 0.0233975342746061, 5.9329575793533079e-05},
      {93628, 0.022708205443012074, 5.9329575793533079e-05},
      {93632, 0.022987006343359935, 5.9329575793533079e-05},
      {93635, 0.02284888479639861, 5.9329575793533079e-05},
      {93640, 0.024373337425823614, 5.9329575793533079e-05},
      {93642, 0.023901422140372417, 5.9329575793533079e-05},
      {93658, 0.025171373030489053, 5.9329575793533079e-05},
      {93660, 0.024253120523838757, 5.9329575793533079e-05},
      {93662, 0.025148352772662166, 0.00011865915158706616},
      {93666, 0.024872109678739512, 5.9329575793533079e-05},
      {93667, 0.024249283814200943, 5.9329575793533079e-05},
      {93671, 0.025682934315531, 5.9329575793533079e-05},
      {93680, 0.024778749744219359, 5.9329575793533079e-05},
      {93691, 0.025340188254552896, 5.9329575793533079e-05},
      {93693, 0.0245268058113362, 5.9329575793533079e-05},
      {93705, 0.022731225700838961, 5.9329575793533079e-05},
      {93721, 0.022387200736648249, 5.9329575793533079e-05},
      {93728, 0.02274657253939022, 5.9329575793533079e-05},
      {93729, 0.022609729895641497, 5.9329575793533079e-05},
      {93742, 0.020889605074687949, 5.9329575793533079e-05},
      {93748, 0.0201414466953141, 5.9329575793533079e-05},
      {93760, 0.017899529363617762, 0.00011865915158706616},
      {93768, 0.020003325148352773, 5.9329575793533079e-05},
      {93769, 0.017639912011458973, 5.9329575793533079e-05},
      {93774, 0.017509463883773276, 5.9329575793533079e-05},
      {93784, 0.01682013505217925, 5.9329575793533079e-05},
      {93792, 0.015418457131164314, 5.9329575793533079e-05},
      {93796, 0.014048751790464498, 5.9329575793533079e-05},
      {93807, 0.013676590955596481, 5.9329575793533079e-05},
      {93824, 0.011989717618170657, 5.9329575793533079e-05},
      {93846, 0.009577706159197872, 5.9329575793533079e-05},
      {93872, 0.0071580212809494578, 5.9329575793533079e-05},
      {93874, 0.0069943216697360344, 5.9329575793533079e-05},
      {98312, 0.071954931450787823, 0.95474339958469312},
      {99820, 0.14421679967260079, 0.0058142984277662381},
      {99888, 0.041765142214037237, 0.00065262533372886387},
      {99908, 0.013143288315940249, 0.00041530703055473156},
      {99920, 0.012938663801923472, 0.00023731830317413232},
      {99932, 0.0055031205238387556, 5.9329575793533079e-05},
      {99940, 0.0087899017802332731, 0.00035597745476119848},
      {99944, 0.0045899836300388784, 5.9329575793533079e-05},
      {99948, 0.0050158583998363, 5.9329575793533079e-05},
      {99956, 0.0091838039697155725, 0.00017798872738059924},
      {99964, 0.0047434520155514633, 5.9329575793533079e-05},
      {99968, 0.00919659300184162, 0.00017798872738059924},
      {99972, 0.0045938203396766932, 5.9329575793533079e-05},
      {99976, 0.0051463065275219972, 5.9329575793533079e-05},
      {99992, 0.0089395334561080415, 0.00011865915158706616},
      {99996, 0.0045938203396766932, 5.9329575793533079e-05},
      {100000, 0.0046245140167792105, 5.9329575793533079e-05},
      {100004, 0.005056783302639656, 5.9329575793533079e-05},
      {100019, 0.013319776959279722, 0.0002966478789676654},
      {100032, 0.0088474524248004921, 0.00023731830317413232},
      {100036, 0.00487134233681195, 5.9329575793533079e-05},
      {100060, 0.0094024964190710051, 0.00023731830317413232},
      {100072, 0.0044927869858809085, 5.9329575793533079e-05},
      {100076, 0.0055721812973194189, 5.9329575793533079e-05},
      {100079, 0.0050030693677102517, 5.9329575793533079e-05},
      {100088, 0.0051987415592387965, 5.9329575793533079e-05},
      {100092, 0.0047856558215674241, 5.9329575793533079e-05},
      {100096, 0.0054621956210354, 5.9329575793533079e-05},
      {100128, 0.021810415387763453, 0.00035597745476119848},
      {100160, 0.017451913239206057, 0.00023731830317413232},
      {100169, 0.0049148250460405154, 5.9329575793533079e-05},
      {100171, 0.00457975240433804, 5.9329575793533079e-05},
      {100172, 0.0050414364640883978, 5.9329575793533079e-05},
      {100180, 0.0045567321465111521, 5.9329575793533079e-05},
      {100193, 0.0046002148557397178, 5.9329575793533079e-05},
      {100254, 0.0091339267444239813, 0.00011865915158706616},
      {100256, 0.0046897380806220582, 5.9329575793533079e-05},
      {100258, 0.0047728667894413749, 5.9329575793533079e-05},
      {100295, 0.0047012482095355025, 5.9329575793533079e-05},
      {100298, 0.0047038060159607124, 5.9329575793533079e-05},
      {100301, 0.0046411397585430737, 5.9329575793533079e-05},
      {100331, 0.0046999693063228976, 5.9329575793533079e-05},
      {100343, 0.0051616533660732555, 5.9329575793533079e-05},
      {100352, 0.0046321874360548392, 5.9329575793533079e-05},
      {100390, 0.012494884387149581, 0.00017798872738059924},
      {104864, 0.23107351135666052, 0.061750222485909258},
      {131072, 0.22779056680990376, 1.2602551171759131},
      {131088, 0.0018262737875997543, 0.23589439335508752},
      {132686, 0.37990459382033959, 0.037116582616434281},
      {136010, 0.59250434827092269, 0.030091960842479976},
      {142254, 0.2541513198281154, 0.040818748145950746},
      {187250, 0.23310952527112741, 0.19045980421239994},
      {187255, 0.0050248107223245346, 7.119549095223969e-05},
      {187259, 0.0046986904031102927, 3.5597745476119845e-05},
      {187261, 0.0042280540208717, 3.5597745476119845e-05},
      {187320, 0.032911295273173727, 0.0002135864728567191},
      {187391, 0.01270718232044199, 0.0002135864728567191},
      {193260, 0.0395628708819316, 0.0045209136754672209},
      {262144, 0.221970278289339, 14.381809552061702},
      {262160, 1.5346838551258442e-05, 0.10509641056066449},
      {343801, 0.0669390730509515, 0.12659744882824095},
      {344423, 0.044713014119091447, 0.0031563334322159621},
      {524288, 0.022378248414160022, 0.13393058439632158},
      {1048576, 0.020636382238592182, 0.14325719371106505},
      {1048584, 2.55780642520974e-06, 0.80379709285078615},
      {1108991, 0.0032420196439533438, 0.01217442895283298},
      {1108992, 0.00045528954368733376, 1.1865915158706616e-05},
      {2097152, 0.040582156742377737, 0.71030554731533735},
      {2097212, 2.55780642520974e-06, 0.015295164639572827},
      {2097376, 2.55780642520974e-06, 0.017063185998220112},
      {2097395, 2.55780642520974e-06, 0.01395431622663898},
      {2098540, 4.8598322078985069e-05, 0.095983387718777791},
      {2099148, 1.7904644976468182e-05, 0.048851972708395142},
      {2183168, 0.0058957438101084518, 849.06589142687642},
      {4194259, 0.0025769899733988117, 0.0092198160783150372},
      {4633128, 0.0020296193984039291, 0.0002017205576980124},
      {4746967, 0.0017150092081031306, 0.00017798872738059921},
      {6864925, 0.00050388786576631883, 0.00043903886087214488},
      {26487398, 0.00010487006343359935, 7.119549095223969e-05},
      {26487399, 9.2081031307550643e-05, 2.3731830317413231e-05},
      {26555190, 9.5917740945365254e-05, 5.9329575793533079e-05},
  };
  return e;
}

EmpiricalProfile Uniform() {
  static constexpr EmpiricalData::Entry e[] = {
      {1, 16620.510133144369, 1518.9533657518678},
      {2, 2785.6481613396486, 250.30983921152162},
      {3, 1122.6188472009846, 777.79203696458183},
      {4, 25400.789458471638, 60929.119836789447},
      {5, 920.8508279565882, 924.31494419913179},
      {6, 1773.7519207101034, 1925.5542824138765},
      {7, 7916.9849420057435, 1417.6084437240327},
      {8, 122313.88415320926, 64746.018333240179},
      {9, 8441.8308749487187, 5717.4433886684183},
      {10, 719.32838734942, 5014.7441916792432},
      {11, 772.18381195688653, 4127.0598811320406},
      {12, 1000.6570954387797, 3792.4994690067633},
      {13, 158.20094916644911, 2860.2478713692171},
      {14, 134.43113788087868, 3306.5322974307378},
      {15, 174.94388542870996, 3172.219495835895},
      {16, 72701.6362417484, 138050.31691912134},
      {17, 24408.18488046843, 149148.4340729976},
      {18, 6029.9095718494764, 18674.036741005719},
      {19, 8470.94264162906, 21109.989193821846},
      {20, 8361.130860030582, 52629.304100758294},
      {21, 3755.5976653116027, 10979.141151044287},
      {22, 47156.676147764141, 17260.102211540252},
      {23, 2906.8462033342034, 12980.097274234718},
      {24, 58783.064964755904, 177859.4025301362},
      {25, 15454.366976839592, 30834.324427552026},
      {26, 1955.5268862119121, 11199.236431725449},
      {27, 1690.543807108492, 7483.9602966109587},
      {28, 4522.3754559355539, 10774.011663219868},
      {29, 1338.45224331481, 73001.672181543792},
      {30, 5651.622403311826, 34714.517522776812},
      {31, 97902.530345354869, 211825.19773442886},
      {32, 190903.7152537948, 880182.1195014253},
      {33, 59815.875519337635, 11194.840273508094},
      {34, 2578.5850837280423, 9504.9301511001813},
      {35, 3153.2561238951257, 9686.456989547818},
      {36, 1719.9524764106964, 45054.602369906657},
      {37, 4144.2252564054752, 8314.65116539042},
      {38, 3793.09724387424, 9737.7424962271525},
      {39, 1650.2649796740386, 8628.2289978201334},
      {40, 50162.463277141687, 316602.73739123956},
      {41, 2653.1385055756537, 7668.29247480111},
      {42, 23936.823050386007, 5574.8317589849648},
      {43, 706.63277701115135, 6634.6881486035809},
      {44, 1462.0605956066088, 5549.7997689713638},
      {45, 709.46420766046322, 6332.0747303113294},
      {46, 1198.3102972438742, 5953.7579043466922},
      {47, 1611.1537202103457, 6634.4846757214991},
      {48, 130057.06956513632, 636221.35762860288},
      {49, 761.06165665908327, 12079.484750246866},
      {50, 570.84052138887853, 5042.5250871015223},
      {51, 334.8623317047701, 5711.9499189536637},
      {52, 653.164593667251, 3725.9551170979821},
      {53, 328.40085779286164, 5635.1782087828142},
      {54, 296.32016559131762, 4048.4583868984405},
      {55, 1002.5675213515832, 16809.074618523278},
      {56, 74008.051820012683, 200055.55031393812},
      {57, 255.33328236303285, 6046.8169098056751},
      {58, 315.996501696938, 4216.95940230656},
      {59, 236.55832991459366, 5429.5888808153077},
      {60, 599.88700070861148, 4189.9477018240086},
      {61, 4412.2547290493421, 11655.199932927169},
      {62, 317.14161600716068, 4174.9872002682914},
      {63, 1180.8694924103979, 6627.7229146870868},
      {64, 87239.396261141985, 269198.204013191},
      {65, 2497.8895517099913, 11255.198889572039},
      {66, 353.51163428187817, 7456.2164961898907},
      {67, 460.31289299966431, 7524.4757513088516},
      {68, 169.76571252750531, 3561.9255118961119},
      {69, 842.96893298027078, 8758.0360702774215},
      {70, 1620.4327359862752, 21263.214428110969},
      {71, 1964.7540055197105, 12873.080356976507},
      {72, 25626.002909036662, 71731.242915432347},
      {73, 5786.4097937567594, 5137.8766605183237},
      {74, 234.04874501174803, 3191.0145697091648},
      {75, 1040.1095942266811, 8443.8233189872},
      {76, 340.69065751687612, 2511.4984070202895},
      {77, 1806.1090888747995, 21130.40962867736},
      {78, 159.91484914034237, 2757.9059117247034},
      {79, 393.04668444411294, 4521.2775138337711},
      {80, 6248.0975758027826, 271860.64768132952},
      {81, 329.22153805989632, 4325.3277252994985},
      {82, 181.53705665162423, 2999.3465429545581},
      {83, 459.062288815127, 3994.6725355392841},
      {84, 169.61158766270094, 1759.2696327762562},
      {85, 673.91037183455785, 3256.2204087716354},
      {86, 102.96460299108641, 1507.7442289419262},
      {87, 193.94212322380935, 3832.0440444916439},
      {88, 6903.2242158654381, 84541.061297114},
      {89, 431.31877820460227, 2282.063980027202},
      {90, 115.26723977175251, 1270.0536210012483},
      {91, 202.38525342184761, 2865.6166601456971},
      {92, 125.96108790512065, 1066.7537681888473},
      {93, 186.77225413045912, 2093.417882361709},
      {94, 463.25910192816917, 1048.6425577105808},
      {95, 896.28946593070521, 1402.9360572354815},
      {96, 18386.127641442585, 36901.933989156561},
      {97, 297.26717264013723, 1699.2671175451344},
      {98, 270.02079774736137, 736.55560523913323},
      {99, 127.92639950770149, 1580.1274383768375},
      {100, 988.40746093312941, 963.58381309038066},
      {101, 229.59293066795956, 1328.328973599389},
      {102, 281.39957110356914, 893.89670784193174},
      {103, 227.08598441054713, 1067.6345648650158},
      {104, 4547.7073378585019, 86960.071693402642},
      {105, 141.52746242494314, 1789.5374769437146},
      {106, 69.078896430835783, 672.10155944329551},
      {107, 91.97740275239623, 1013.6468988131835},
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      {32760, 6.4364785738261281, 5.5720194511206733},
      {32768, 156.55965576399507, 135.33607214055485},
      {32769, 4.5774810726140309, 0.001900396847576994},
      {32776, 0.11321933390519524, 4.74719132524733},
      {32810, 0.814873382314549, 1.0524285953831538},
      {33280, 2.6763957781673064, 0.83431147876958667},
      {34816, 4.19472084436654, 7.2227190579993685},
      {36872, 4.5597079774736153, 14.493506977437448},
      {38480, 3.5477604147242006, 4.3186890988020039},
      {40960, 8.2069033677693675, 3.4110446593259161},
      {45056, 8.2943441614142355, 7.2711419149292951},
      {45064, 0.039178756573304, 2.3449779218601532},
      {46800, 2.2239846343191743, 14.204628025264091},
      {48360, 2.7282307089844471, 2.7146982654220935},
      {49152, 7.3407787267370335, 7.6827082518212153},
      {49208, 0.18639652407414312, 6.7531906172563492},
      {49216, 7.8274344534367657, 1.2262403815698768},
      {49384, 0.21929474508633873, 1.8510051608816367},
      {53248, 3.9779230224145, 9.1221284444692934},
      {53412, 0.13759743408048336, 1.126842173904943},
      {57344, 15.833060455749077, 10.481676075494203},
      {58280, 0.761089769887741, 2.1136698153634028},
      {58752, 0.46597918919926906, 1.1797924468540952},
      {61441, 7.5596538992279854, 4.7604941031803731},
      {65160, 10.842690113004888, 11.626572019451125},
      {65532, 244.99021556707567, 1.5798073519274118},
      {65536, 381.6361242680789, 120.36746595122314},
      {65537, 2.7484093536717262, 0.990088126245971},
      {65544, 2.00492671465334, 0.2189741583291413},
      {65552, 22.423496065341443, 0.991764946993833},
      {65578, 1.6389139596464402, 0.11167626180761277},
      {69632, 11.475260135009137, 4.0189294431092},
      {73728, 3.5588856151866621, 2.9022227190579986},
      {74256, 0.53680117853280107, 1.2223277998248656},
      {76416, 2.3946294707790994, 0.7517187412665588},
      {76490, 21.188680863760119, 0.053155217707227115},
      {81920, 8.24725319807556, 3.7676671697128921},
      {81992, 0.65109461828217641, 91.9023158757662},
      {86016, 3.5146980942080326, 2.2041622417230262},
      {86320, 0.29318800581807336, 0.995826579471988},
      {87296, 26.043096632230622, 0.87349319024462946},
      {90112, 3.1136053406929469, 1.0897099100106191},
      {92160, 1.576640062656175, 1.1471689676373586},
      {98232, 6.6123671353447957, 3.5180258230395172},
      {98304, 3.32476224219595, 2.7284854582378508},
      {98312, 0.084248312385783036, 3.9911128500363313},
      {98806, 1.3028381755118785, 0.68624820673336673},
      {104000, 1.3973427068959092, 5.396586738211016},
      {104864, 1.208065117666804, 0.14252976356827454},
      {122881, 4.0822567411330315, 4.0069494904328078},
      {131072, 50.996658337373653, 28.539116501779269},
      {131073, 0.20920821989333532, 0.0033909041790099307},
      {131088, 26.749966434192366, 0.8954781733832653},
      {131114, 0.47100846604259133, 0.0027388072215080205},
      {131574, 0.21183008242270535, 0.053770051981443204},
      {132570, 0.0989892962369, 0.62556592700240421},
      {139264, 0.63846455077760844, 2.2698749836975769},
      {142144, 0.2646104501547758, 1.2411454548842078},
      {163840, 2.8104986387200239, 2.58055260559313},
      {163841, 0.12443404318800581, 0.0014346133065042013},
      {166024, 0.23233506135083729, 0.6042889348461985},
      {180224, 1.6585574161787187, 1.4952955862351649},
      {196608, 2.4342016932085184, 17.632664468168358},
      {196615, 0.97317159586767621, 0.29055577292120804},
      {196744, 0.011483235743855591, 0.66074190002422084},
      {196880, 1.0934639913474806, 0.029884671995230379},
      {245761, 2.0413437511654795, 3.3665716468242874},
      {245816, 0.0019374930071234104, 0.4410970133959346},
      {262140, 2.0220807071196805, 0.96018482290909835},
      {262144, 26.314778279192929, 9.8597059974288754},
      {262148, 4.8937381121097978, 0.40953552065284221},
      {262160, 7.5692574497445264, 0.75022823393512572},
      {262168, 7.01986909335024, 0.013619510740968458},
      {262186, 0.26825234028269862, 0.0031486967376520786},
      {262265, 0.86895349270876043, 1.4840236245412031},
      {262661, 0.24451758475366425, 0.21994298809457263},
      {262805, 0.20084473949203746, 0.27155180444543808},
      {278528, 0.45082795658822222, 1.7952415553444008},
      {279656, 0.041006228322082554, 0.354852532930896},
      {327680, 0.99564763361056241, 1.6317887951111367},
      {327687, 2.9140193189870582, 0.17161328787285973},
      {342446, 1.0110431507104769, 0.45590893000204957},
      {347523, 0.28648789766158228, 0.16798017625249198},
      {352456, 0.07721254615298552, 0.5143181860525774},
      {360448, 0.43015514862193704, 0.20708736236096373},
      {361401, 0.16511953157050685, 0.024388426210571419},
      {379184, 0.1721124081602208, 0.67035567231196314},
      {393216, 0.64773617275202289, 0.737782497717661},
      {393224, 0.030559803080595232, 1.3647457753432823},
      {393256, 0.00060231977026069445, 2.0841577702010321},
      {491521, 0.79714504158430644, 2.3354945689639126},
      {520961, 0.1531477268489165, 0.958694315577665},
      {524288, 10.085525677842844, 11.051739235742374},
      {524289, 0.054031626449856415, 0.0040616324781547518},
      {524304, 5.4992596874650355, 0.75041454735155477},
      {524330, 0.1257561630552344, 0.0026083878300076392},
      {589831, 2.7725058740163373, 1.0156130642967607},
      {655360, 0.22677246111960619, 0.5705662064725282},
      {720896, 0.26148323574385535, 0.55595923462448538},
      {786432, 0.213029127661955, 0.51539880386786652},
      {786536, 0.00080557938313504643, 2.0789037318577339},
      {800008, 0.026742624846156731, 1.3021258360814549},
      {917512, 0.10243538582031103, 0.5281426415516185},
      {925639, 0.004900607914071535, 0.13464870605332277},
      {983040, 0.032284712639391346, 0.270098559797291},
      {983041, 0.01751762204900608, 0.21809848527192444},
      {1039269, 0.029183604967739529, 0.2393568460864868},
      {1040659, 0.0011169954872636411, 0.059489873865816972},
      {1040667, 2.2377205087084623e-05, 0.10729789652152852},
      {1048576, 13.446264871517545, 77.237493711922269},
      {1048580, 0.00416216014619774, 0.056452965178022466},
      {1048584, 0.000251743557229702, 0.9217669964414138},
      {1048592, 0.83427628389214192, 21.545637471354311},
      {1048618, 0.047199119829933238, 0.0005962029325731746},
      {1114119, 1.1258866967515762, 0.18825107595997992},
      {1310720, 0.066010890239809022, 0.41301958154006679},
      {1441792, 0.10249319360011935, 1.1478024332532188},
      {1572864, 0.068284041323238662, 0.19721275129022056},
      {1572904, 0.00032633424085331739, 0.038715927933970523},
      {1835008, 0.023992093387535898, 0.18661151789540356},
      {1835016, 0.00013053369634132697, 0.01900396847576994},
      {1966080, 0.012244060716816472, 0.263111806681199},
      {1966081, 0.0041808078171036434, 0.11076332606711009},
      {2097151, 0.0090776861969939955, 0.099770834497792144},
      {2097152, 0.91072800507216645, 2.4636409367838579},
      {2097153, 0.60188527952858684, 0.1672908166117042},
      {2097160, 3.3565807630626934e-05, 0.64449537011160174},
      {2097168, 0.1401055458173274, 0.13680994168390065},
      {2097194, 0.014121881177040987, 0.00087567305721685039},
      {2129920, 0.02172640137246858, 0.56624373521137239},
      {2162695, 0.29806810129414912, 0.58543401710357312},
      {2236962, 0.0016559131764442617, 0.095765096044566178},
      {2276907, 0.00075150113750792574, 0.078382054291729661},
      {2318306, 0.00083355088949390265, 0.14830547947757688},
      {2339575, 0.00064147987916309262, 0.14996366888379631},
      {2361237, 0.00035990004848394447, 0.18636931045404564},
      {2369250, 0.60185917278931855, 0.16555810183891331},
      {2383305, 0.00029276843322269041, 0.15991280532111093},
      {2405789, 0.000328199007943908, 0.13749930132468813},
      {2621440, 0.0098273225674113361, 0.15169638365658705},
      {2883584, 0.01674747324059225, 0.059024090324744261},
      {3145728, 0.023999552455898254, 0.1591861829970376},
      {3145928, 0.00023682542050497892, 0.089262757811189988},
      {3670024, 0.0058535038973632231, 0.1553667579602406},
      {3932161, 0.0023980904784992336, 0.15089523596594187},
      {4194304, 0.18640025360832427, 0.7638477446760944},
      {4194320, 0.037310259948532432, 0.090212956234978492},
      {4194346, 0.014478051691343752, 3.7262683285823413e-05},
      {4259847, 0.064457539253347212, 0.021239729472919328},
      {4718592, 0.0011095364189012793, 0.042740297728839423},
      {4793490, 0.00015850520270018273, 0.013917612207255046},
      {4971026, 0.00060045500317010454, 0.016693682112048882},
      {5162220, 0.00057248349681124865, 0.017029046261621276},
      {5242880, 0.0035393279379405495, 0.10368341624280369},
      {5253684, 2.6106739268265396e-05, 0.9249529558623516},
      {5368709, 0.0002237720508708462, 0.018854917742626622},
      {5592405, 0.00080930891731622733, 0.0190971251839845},
      {5767168, 0.0028680117853280116, 0.017308516386264964},
      {5835553, 0.00010069742289188079, 0.013619510740968458},
      {6100805, 0.00054824152463357355, 0.015426750880330894},
      {6291456, 0.0053537463170849958, 0.020792577273489463},
      {6291464, 2.6106739268265392e-05, 0.014774653922828982},
      {6391320, 0.00019207101033080962, 0.021500568255920106},
      {6710886, 0.00044567933465110223, 0.023922642669498596},
      {7064090, 0.00040092492447693303, 0.013004676466752374},
      {7083713, 4.8483944355350019e-05, 0.013358671957967694},
      {7255012, 0.00015291090142841154, 0.0079928455648091232},
      {7309400, 5.780777980830194e-05, 0.007173066532521007},
      {7354396, 0.00012680416216014618, 0.014476552456542396},
      {7500402, 0.0001790176406966769, 0.015911165763046596},
      {7561562, 8.3914519076567343e-05, 0.038119725001397362},
      {7780737, 0.00022004251668966536, 0.015724852346617475},
      {7864320, 0.040465445865811349, 1.1380396102323325},
      {7864321, 0.00020885391414612314, 0.041585154546978927},
      {7895160, 8.018498489538655e-05, 0.01278110036703743},
      {8194304, 0.00061350837280423716, 0.016973152236692542},
      {8257085, 0.00016409950397195387, 0.010284500586887263},
      {8388608, 0.11147577667549316, 0.3524490898589609},
      {8405001, 6.9988438444038339, 0.01266931231717996},
      {8454151, 0.017512027747734298, 0.015147280755687217},
      {8947848, 0.00056502442844888706, 0.016861364186835096},
      {9437184, 0.00034311714466863112, 0.047323607772995747},
      {9808218, 0.00028344459776973854, 0.010452182661673469},
      {10485760, 0.0016876142169842971, 0.069401747619846188},
      {11534336, 0.0016018349308171388, 0.070799098243064587},
      {12582912, 0.0022022899339872444, 0.01516591209733013},
      {12582952, 2.7971506358855779e-05, 0.028114694539153766},
      {12582960, 7.4590683623615413e-06, 0.0057011905427309818},
      {14235768, 0.00060045500317010465, 0.15616790565088562},
      {14680064, 0.00013426323052250771, 0.012538892925679579},
      {15728640, 0.00038787155484280015, 0.27734615169638366},
      {15728641, 0.00010256218998247119, 0.0081232649563095036},
      {15790320, 8.5779286167157726e-05, 0.011644588526819816},
      {16515073, 0.00024987879013911162, 0.0079742142231662115},
      {16777216, 0.0375862454779398, 0.16894900601792331},
      {17825792, 0.0078935590944691023, 0.68145995193113862},
      {18874368, 0.00014172229888486927, 0.015352225513759246},
      {19173961, 1.8647670905903854e-05, 0.0027574385631509326},
      {20971520, 0.00045127363592287331, 0.047025506306709153},
      {21251140, 0.00014545183306605006, 0.0025524938050789036},
      {22369621, 0.00021817774959907507, 0.0036890056452965176},
      {23068672, 0.000634020810800731, 0.13066159894173976},
      {25165824, 0.0008074441502256371, 0.011085648277532466},
      {26843545, 0.00018461194196844809, 0.20701283699439185},
      {31457280, 0.00076641927423264848, 0.075717772436793188},
      {31457281, 6.8996382351844252e-05, 0.0034281668622957538},
      {31876710, 0.00051654048409353675, 0.0083282097143815327},
      {33554432, 0.023665759146682556, 0.42267061651109528},
      {37748736, 0.0001603699697907731, 0.019581540066700202},
      {41943040, 0.00010069742289188078, 0.0081232649563095036},
      {42502280, 0.00018274717487785786, 0.013507722691110988},
      {44739242, 0.00046432700555700608, 0.004620572727442103},
      {46137344, 6.3402081080073089e-05, 0.05362100124829991},
      {49807360, 0.00016036996979077324, 0.0084586291058819148},
      {50331648, 0.00022936635214261742, 0.15758388761574715},
      {51002736, 5.4078245627121168e-05, 0.0073966426322359478},
      {53687091, 0.00014545183306605012, 0.0024593370968643462},
      {59652323, 0.00012307462797896536, 0.0029064892962942269},
      {63753420, 0.001282959758326185, 0.20988206360740036},
      {67108864, 0.026058255323910033, 0.34272352952136109},
      {75497472, 5.03487114459404e-05, 0.014867810631043542},
      {76695844, 2.7971506358855779e-05, 0.0035585862537961359},
      {83886080, 3.3565807630626934e-05, 0.0014718759897900248},
      {85004560, 3.5430574721217324e-05, 0.0014159819648612898},
      {89478485, 4.6619177264759629e-05, 0.0059433979840888343},
      {92274688, 1.3053369634132696e-05, 0.010899334861103348},
      {100663296, 5.4078245627121168e-05, 0.0014532446481471133},
      {107374182, 2.7971506358855782e-05, 0.0083654723976673562},
      {127506840, 0.0039141461231492185, 0.109515026177035},
      {134217728, 0.0059206355126244737, 0.20990069494904329},
      {134217736, 2.7971506358855779e-05, 0.0048814115104428672},
      {150994944, 1.6782903815313467e-05, 0.008868518622025973},
      {167772176, 2.4241972177675009e-05, 0.002869226613008403},
      {178956970, 4.8483944355350012e-05, 0.0038194250367968997},
      {214748364, 1.3053369634132696e-05, 0.002161235630577758},
      {251658241, 1.1188602543542311e-05, 0.045795837758276975},
      {255013680, 0.0023757132734121508, 0.092262403815698765},
      {268435456, 0.00085965762876216766, 0.024798315726715481},
      {357913941, 9.3238354529519217e-05, 0.0012669312317179968},
      {503316481, 1.3053369634132696e-05, 0.00026083878300076389},
      {510027360, 9.1373587438928875e-05, 0.010452182661673467},
      {536870912, 0.0088856151866631809, 0.078717418441301992},
      {993774200, 1.8647670905903854e-05, 0.00022357609971494048},
      {1073741824, 0.00027225599522619627, 0.0092597767965271176},
      {1073741825, 1.8647670905903853e-06, 0.00011178804985747024},
      {2147483647, 1.3053369634132696e-05, 0.0028878579546513143},
      {2147483648, 1.6782903815313467e-05, 0.0018817655059340823},
      {5989689812, 1.8647670905903853e-06, 1.8631341642911706e-05},
      {6427011476, 1.8647670905903853e-06, 1.8631341642911706e-05},
      {6869701940, 3.7295341811807706e-06, 3.7262683285823413e-05},
      {10285464124, 1.8647670905903853e-06, 1.8631341642911706e-05},
      {10285464164, 1.8647670905903853e-06, 1.8631341642911706e-05},
      {11543619396, 1.8647670905903853e-06, 1.8631341642911706e-05},
      {11612973992, 3.7295341811807706e-06, 3.7262683285823413e-05},
      {15922538564, 3.7295341811807706e-06, 3.7262683285823413e-05},
  };
  return e;
}

}  // namespace empirical_distributions
}  // namespace tcmalloc
